Iwona Dudek
email: iwona.dudek@map.cnrs.fr

Spotting temporal co-occurrence patterns: the historySkyline visual metaphor

. It aims at helping analysts get a better overview of potential temporal interactions -and as such basically aims at uncovering new research questions.

Abstract -When trying to depict how architecture gets transformed over time, it is important to try and spot and analyse temporal relations between architectural changes on one hand and facts or events that may have triggered or at least impacted on these changes. In this contribution we introduce a visual metaphor called historySkyline aimed at aligning in time architectural events (any changes, including destruction or extension) and facts that may have impacted these events (in short, pieces of information about historical contexts). Visual metaphors are commonly used to uncover temporal patterns in the field of information visualisation (Infovis). Our experiment, carried out on the historic centre of the city of Cracow, shows that such an approach can be worth trying out in the context of historical sciences, and underlines some of the specific challenges this application field raises.

I. INTRODUCTION

When trying to understand and recount how pieces of architecture get transformed as time passes by (may we observe one particular historic edifice or a whole urban structure), analysts pull together a variety of documentary hints helping them to spot and depict changes over time, and to order (if not date) those changes. The word "changes" means here of course morphological or structural modifications such as extensions or demolitions, addition of new architectural components or removal of deprecated technical solutions, replacement of a material by another, etc.. But it may also refer to successive functions devoted to a piece of architecture or to successive ownerships and role in the city for instance. At the end of the day, analysts try to end up with a sort of "chain of events" where periods of stability and changes are assessed and ordered in time, and where the actual physical layout of pieces of architecture is likely to be represented in 2D or 3D through contemporary geometric modelling platforms (typically, VR applications). But when looking at it from closer, what exactly are architectural changes? A random, accidental,

II. METROLOGY AND THE TIME PARAMETER

Metrology, pointed out in Wikipedia as the "the science of measurement", has paved its way on top of the research agenda when facing the necessity to acquire and spatial data, with technologies like photogrammetry and laser scanning nowadays widespread in archaeology. But beyond spatial features, measuring the time parameter is also an issue, with well-established "absolute" methods like radiocarbon dating or dendrochronology to human cantered observation methods on for instance a stratigraphy. These examples in fact illustrate some of the models of temporal data that are summarized in [START_REF] Aigner | Visual Methods for Analyzing Time-Oriented Data[END_REF] [START_REF] Aigner | Visual Methods for Analyzing Time-Oriented Data[END_REF][5] can be of great use in processing temporal metrology-based information. But when trying to pull together pieces of data corresponding to strongly heterogeneous acquisition processes, another methodological challenge is raised: coping with unevenly defined data sets. When talking about spatial data, this can occur for instance when handling on one hand a contemporary photogrammetric survey and on the other hand a human witness report saying "three minutes away from...". In the same way this can happen when handling temporal data, with for instance a one year match for artefacts made from wood, only relative dating like contextual seriation for a piece of stonework, or even human reports. This is precisely what happens when wanting to cross-examine a large amount of information on the changes over time of a large site like Cracow's market square, with hints ranging from archival material to contemporary archaeological findings. Our focus in this paper is put on the cost and constraints of reasoning on such data sets, an issue that we believe is a relevant one in historical sciences at large where gaining insight does not only depend on the accuracy of an instrument, but is impacted by the heterogeneity of the temporal data. What we therefore investigate is not the temporal data acquisition itself, but the way diversely acquired temporal data can at the end of the day be merged so as to spot temporal cooccurrences.

III. THE CONTRIBUTION

We introduce a visual metaphor called historySkyline aimed at aligning in time architectural events (any transformation, including destruction or extension) and facts that may have impacted these events (in short, pieces of information about historical contexts). The visualisation combines a recount over time of architectural transformations (by type) with indications on the amounts of historical evidence available and with a variety of contextual information such as wars, natural disasters, reign of rulers, demography, new laws, etc.. The visualisation does not actually mention causality: it barely puts facts that occurred at the same period side by side. It is applied to architectural transformations on Cracow's Main Square (over 40 edifices at one time, 3 left today -371 architectural transformations recorded, 538 bibliographic sources, 478 pieces of information about various elements of contextualisation). It builds on an infovis-birthed mantra: using vision to think [START_REF] Card | Readings in Information Visualization: Using Vision to Think[END_REF], with here a specific bottleneck -highly heterogeneous data sets. The contribution introduces the methodological and technological choices behind the historySkyline visual metaphor, and discusses its practical benefits and limitations in terms of information discovery on the abovementioned test field.

IV. VISUAL METAPHORS

The notion of visual metaphor stems from the Infovis and visual analytics communities. The information is displayed using a real-world equivalent, like for instance the image of a tree with branches to convey an information about a genealogy, a long time used metaphor as shown in [START_REF] Rosenberg | Cartographies of Time: A History of the Timeline[END_REF]. Visual metaphors are, as mentioned in [START_REF] Kienreich | Information and Knowledge Visualisation: an oblique view[END_REF], one of the three fundamental units of visual representation in Infovis, along with formalisms (a pie chart for instance) and models (when the information itself is based on a real-world equivalent like in the "Brockhaus Planetarium" space Atlas [START_REF] Kienreich | Information and Knowledge Visualisation: an oblique view[END_REF]). Most often the

Fig. 1. A zoom on the historySkyline visual metaphor. The building activity on the Market Square in Cracow (blue vertical bars, year per year) is correlated with the Czech occupation (symbol composed of a red arc and two dots showing the time interval)

design of a visualisation implies combining these unitsand the historySkyline visualisation does include both a main metaphor -the image of an urban skyline, and its reflection in the water, and visual formalismsdiagrammatic shapes in the bottom part.

Visual metaphors are commonly used in the above mentioned communities in the handling of the time parameter. A great number of historic examples for genealogies (tree, chain, hand, etc.) or time charts (ladder, river, temple, game of snakes and ladders, etc.) are illustrated in [START_REF] Rosenberg | Cartographies of Time: A History of the Timeline[END_REF] and [START_REF] Tufte | The visual display of quantitative information[END_REF] (conf. Fig. 2).

Contemporary, computer-born, 2D or 3D examples are also quite numerous such as Infosphere [START_REF] Blaise | Infosphere: one artefact, two metaphors, three sort criteria[END_REF], Datavases [START_REF] Thakur | Data Vases: 2D and 3D Plots for Visualizing Multiple Time Series[END_REF], TimeWheel or Perspective walls, [START_REF] Aigner | Visual Methods for Analyzing Time-Oriented Data[END_REF] etc..

A key aspect in the design of any temporal data visual metaphor is to understand the model of time corresponding to the underlying data. For instance, a tree metaphor for genealogies uses an "ordinal time" scale, as defined by [START_REF] Aigner | Visual Methods for Analyzing Time-Oriented Data[END_REF], i.e. t 1 appears before t 2 whether or not t 1 and t 2 are actually dated. By contrast, time charts use a "discrete time" scale where time is mapped to a continuous series of Integers (typically, a year, a day, etc.), implying that each piece of data is dated. Similarly choices are made in terms of granularity: a smallest unit (called chronon) needs to be fixed, for instance a day in classic calendars. The choices we have made are discussed in the next section with regards to the data we handle.

V. THE DATA The baseline objective of the historySkyline visual metaphor is to allow the spotting of temporal cooccurrences between architectural changes and broadly speaking a context. In the list below we show the various types of data that we pulled together, and for each of them the main corresponding models. > time intervals, in years 5. military events (siege, occupation, assault, invasion, etc.), > time points or time intervals, from days to years 6. natural disasters (floods, fires, epidemic, gale, famine, etc.) -unevenly dated in sources beyond their intrinsic heterogeneity, > time intervals, from days to years 7. legal matters (decrees, limitations, privileges, etc.) with in sources an accuracy of dating ranging from a day to a year, > time point, a year 8. global military context in the country (significant battles, sieges, etc.), > time intervals, from days to years 9. population in Kraków,

> time point, a year

The variety of the models themselves, but above all the variety in terms of precision of the data we handle made it clear that the most reasonable choice to adopt was to stick to a discrete time model, with a one year chronon. Limits of this choice are discussed in the conclusion section. The choice of a discrete time model with a one year chronon does not impact the way we store the data itself: it impacts the way the results of queries on these databases are exploited: each piece of data has to be "translated" to match the model.

VI. FROM THE DATA TO THE VISUALISATION

The visualisation is calculated in real time, not drawn once for all (infrastructure RDBMS/Perl/SVG). It uses Fig. 3. The Infosphere visual metaphor uses the image of a globe, with parallels and meridians used to sort pieces of information, and rings that correspond to periods. VII. EXAMPLES OF USE At this stage the historySkyline visualisation is basically a proof-of-concept prototype, experimented on a specific case study. It would definitely require a thorough evaluation effort before stating whether the approach can be generalised. It has however been tested in the context of workgroup discussions in order to evaluate to which extent the visualisation can support information discovery (e.g. identifying unexpected temporal co-occurrence patterns). As an illustration, three interesting patterns spotted during these workgroup discussions are presented below, along with the open questions they helped raise. These three examples underline what are probably the most beneficial results of the approach: highlighting, pointing out unaddressed research questions, needing further investigation, as well as corroborating assumptions and intuitions.

VIII. CONCLUSION The historySkyline visual metaphor has been designed as a tool helping analysts to cross-examine strongly heterogeneous temporal indications, allowing a bridging of the "quality gap" between metrology-based temporal data, and various historical hints. Temporal relations between facts and events can be observed, in order to spot temporal co-occurrences laid before the eye of the analyst as question marks. To conclude, a number of limitations must be pinpointed. In terms of technology, such a visualisation requires a high level of interaction so as to allow users to dig deeply into the data displayed (selective zooming, multiple selections, etc.). Moreover, a key limit in terms of method is the time model we have adopted -discrete time, with a one year chronon. Such a choice implies for instance that we cannot visually discriminate an event that occurred in spring from an event that occurred in autumn. It also implies transferring qualitative temporal information such as "beginning of the 14 th century" into quantified intervals. Finally, the uncertainty of dating, visualised through specific symbols, results in potentially deceptive time intervals, and thereby in possibly misleading temporal co-occurrence patterns. For all these reasons the historySkyline metaphor should be considered as a first step, needing further investigation. Among the main perspectives ahead is the idea of testing the ordinal time model. Ultimately, and because the objective is to support analysts in their reasoning tasks, we consider a key aspect in the development of such a visualisation is to allow a user monitoring of the interpretative steps -for instance giving each user the possibility to test alternative interpretations of uncertain dating. On the overall the approach appears promising, yet underlines to which extent merging heterogeneous temporal data sets remains a challenging issue.

1 .

 1 architectural changes (in terms of morphology, structure, function or ownership), > time intervals, in years 2. certainty of dating for morphological changes (a 3 values scale) indicating to which extent the left and right bounds of the above interval are trustworthy indications, > time point, a year 3. period of reign of rulers, > time intervals, in years and days 4. amount of sources used to document the changes (grey reflection of the skyline)

Fig 2 .

 2 Fig 2. Emma Willard's 1846 " Temple of Time" : athree-dimensional projection of historical chronography[START_REF] Friendly | [END_REF]

Fig. 5 .Fig. 7 .Fig. 6 .

 576 Fig. 5. General structure of the visualisation. Height of bars show the amount of transformations, year per year (graduation on the y-axis)

Fig. 4 .

 4 Fig.[START_REF] Aigner | Visual Methods for Analyzing Time-Oriented Data[END_REF]. HistorySkyline calculated for one edifice alone, the "Grand Scales".

Fig. 12 .Fig. 11 .Fig. 10 .

 121110 Fig.12. A major fire occurs in 1850, and spreads to several quarters of the city. Although it did not directly impact the major structures of the Market Square's heart, it is followed by a period of destructions (black vertical bars): An economic issue? An opportunity seized by the recent occupying power to refurbish the city centre?

Fig. 9 .Fig. 8 .

 98 Fig. 9. Symbols used to position major military events in time -in this example the 1836-1841 Austrian occupation is highlighted. Purple lines are displayed up to above the horizon line so as to read potential cooccurrences with the information displayed there.

Fig. 13 .

 13 Fig. 13. historySkyline for the Town Hall ensemble (5 edifices), symbol of power in the city. Visible here is a "seizure of power" pattern (a,b,c,d) -numerous functional transformations on the arrival /leave of the occupying force. An exception is highlighted (c) three different occupying powers at the same time. The visualisation corroborates an intuitive assumption that in such a case a status-quo situation may prevent actors from intervening on a symbolic edifice.

  In other words, beyond the field of archaeology, measuring and modelling the time parameter is common in many research fields, like medicine or climate for instance, and contributions like

		:
	▪	Time primitives (what results from radiocarbon
		dating -a date with a "fork" i.e. an interval)
	▪	Granularity (dendrochronology dates per year,
		i.e. single granularity)
	▪	Scale (a stratigraphy says t 1 before t 2 , even when
		neither t 1 nor t

2 are dated, i.e. ordinal time).


Jean-Yves Blaise

Iwona Dudek

and Knowledge Management

There definitely is a lot of information available on the net through airlines reservation systems, airports destination maps, etc. But is that 'space + time' information really synthetic, easy to read ? The very nature of the query one fires on such systems (typically "find flights from A to B on day D, order them by price / duration") strongly impacts the type of information users will retrieve, and the way it will be displayed.

The FlightSchedule Profiler

An attempt to synthetise visually an airport's flight offer in time and space.

Three key choices: stylized cartography, ordinal time model, "details on demand"

Step 1 : The cartographic background. Origindestination vectors intersecting a circle

Step 2 : Redistributing destinations along a second, exterior circle so as to avoid overlapping.

•

  Too much (irrelevant) data, • No overview, no user-side mental image of time + space alternatives, • Lacks … infoVis? Shortly said, such queries end up on: • sequential data seriesone flight after the other, page per page • verbose presentationstime slots and routes are given as texts, temporal densities not assessed • focus viewsdetails on one flight at a time • space parameter limited to a textual list of airports schedule (redrawn and simplified). Time runs horizontally from left to right (24 hour slot, starting 6AM). Railway stations (cities) are distributed vertically. Oblique lines corresponds to trains connecting Paris to Lyon and vice-versa. The angle (a) represents the speed of trains (the duration of the travel in fact). Oblique lines redrawn in black correspond to the fastest trains -the structure of the graphics makes it so that it is simply straightforward to uncover a pattern: these trains depart at the same time. Note that this graphics helps spotting at a glance for instance which of all trains is the slowest (circle "1" above the top horizontal line), or lets you compare the stopover time for each train, in both direction, in all railway stations.

  seasonal or occasional flight destination available on Mondays destination available on other days of the week regular flight (every Monday over the period) Step 3 : Introducing the ordinal time layer (Monday flights) -each coloured dot corresponds to one flight from Nice to a destination airport. "Piles" of coloured dots correspond to destinations for which several flights are available on Mondays, sorted by chronological order (details available on user demand).Note the varying proportion of non-regular flights between those heading north-west and others. User-side interaction triggers the displaying of textual and visual information about cities, airport codes, place types, departure and arrival times, operating periods etc.

1Flying2

  users with a clear-cut visual overview of an airport's flight offer. Our objective: Not replacing but complementing reservation systems in upstream tasks. An extract of the 1933 Czech Airlines map and schedule (redrawn from E.R Tufte, Envisioning information, relative sizes of circles preserved from the original). Each circle corresponds to relative locations in space; departure and arrival times are shown inside the circles, lines with flight codes connect airports (the presence of an arrow differentiates inbound from outbound flights). Brown circles (top left) correspond to the "real" location of cities on a geographic map . This design combines in one unique visualisation parameters space (position of cities) and time -departure / arrival times. There are here readability concerns that could be pointed at -the orientation of departure / arrival times inside circles for instance -but it shows there definitely is room for graphic creativity in the context of travel data. The 'FlightSchedule' proof of concept visualisation -investigating the way travel data can be layer (Monday flights): concentric circles correspond to hours of a day (time runs outwards). Each dot corresponds to a given flight, with the same colour codes as in the ordinal time layer.The visualisation is an attempt at assessing temporal densities throughout the day.

* A tribute to M. Friendly's "The Golden Age of Statistical Graphics"

The FlightSchedule Profiler

An attempt to synthetise visually an airport's flight offer in time and space.

Jean


Vincent Loyau

Victor Morin

Gérard Chaplier

Martino Lobue

Frédéric Mazaleyrat

Magnetoelectric effect in

I. Introduction

Magnetoelectric 1 (ME) materials which exhibit a coupling between magnetic properties and dielectric properties have a great interest due to their potential use in smart electronic applications. The ME effect consists in an electric polarization change when a magnetic field is applied (direct effect) or, conversely, a magnetization change when an electric field is applied (converse effect). Intrinsic (single phase) ME coupling was first detected in Cr 2 O 3 at low temperature, but the effect is very weak and it cannot be used in electronic devices. More recently, both ferroelectric and ferromagnetic properties were discovered in bismuth ferrite 2 at room temperature, however the observed ME magnitudes are still too weak for application purposes. Recently, intrinsic ME effect suitable for some application has been reported in materials 3 derived from barium zirconium titanate with a small substitution of Fe. A possible alternative to the research of new intrinsic ME materials with enhanced effect is represented by the use of magnetostrictive/piezoelectric composites. In this case the ME effect arises through the mechanical coupling between the two phases 4 . When a constant magnetic bias field is applied to the composite, the magnetostrictive material shows a piezomagnetic behavior and the application of a small alternative field gives rise to a corresponding alternative strain. Due to mechanical coupling, an alternative electrical field appears within the piezoelectric phase. ME bulk composites have been made first by sintering together BaTiO 3 or PZT with spinel ferrites. However, the low resistivity of the ferrite that short-cut the piezoelectric phase acts towards a lowering of the ME effect 5 . This difficulty is overcome when using laminated structures 6 .

So, in the 2000s, interest has been focused on layered composite structures based on PZT associated with different ferrimagnetic materials: nickel ferrites, cobalt ferrites, or lanthanum manganites 7 . Although nickel ferrites exhibit much smaller magnetostriction than cobalt ferrites, they show a better ME effect which is further strengthened by zinc substitution 7 . Furthermore, ME coupling seems to be dependent on geometric parameters such as layer thickness, number of layers, and volume ratio of the two phases. Strongest ME effects were obtained for co-sintered thin layers of PZT/nickel-zinc ferrite in the range of 10µm using the tape-casting 8 route. Giant magnetostrictive material such as Terfenol-D (Terbium Dysprosium iron alloy), were also used in laminated configurations associated with PZT or PMN-PT at resonant or sub-resonant frequencies 4,9,10 . Rare earth-iron alloys have been developed to reach large magnetostrictive strains (>1000ppm), and one obtains piezomagnetic coefficients as high as at optimum bias field. Although giant ME coupling was obtained, the use of Terfenol-D is not suitable for the following reasons: (i) this material is extremely brittle and it cannot be machined easily; (ii) it cannot be co-sintered with piezoelectric materials; (iii) its high electric conductivity limits the use at low frequency because of the eddy currents; (iv) terbium and dysprosium is rare and expensive.

A piezoelectric/piezomagnetic bilayer can be modeled as two mechanically coupled transducers. In the 1950s and 1960s, some investigations on cobalt-substituted nickel ferrite transducers were conducted and some materials suitable for underwater applications were obtained 11,12,13 . Although the best composition of ferrite quenched in air achieved a coupling factor as high as 0.37, 12 in the 1960s research has turn towards PZT materials which have better electromechanical coupling. Nevertheless, in the field of ME composite, replacing conventional nickel ferrite with low magnetomechanical coupling factor 11 (k = 0.18) by cobalt-substituted nickel ferrite can lead to an improvement of the ME effect. Piezomagnetism is an intrinsic property which depends on the internal DC Bias and AC exciting magnetic fields. The demagnetizing field [START_REF] Chikazumi | Physics of magnetism[END_REF] , depending on the overall geometry of the system, can greatly influence the ME response of a layered ME composite in the longitudinal as well as the transversal modes. Actually, a layered structure is strongly anisotropic and the demagnetizing field will affect rather differently the response of a system of given diameter and thickness under radial or axial excitations.

In the field of ME laminated composites, some studies have already be made on the influence of the demagnetizing effect (see Ref. 15, 16, and 17), but in these cases only the ME transversal mode was considered. However, here, we developed a simple model to take into account the influence of the demagnetizing field in the ME transversal as well as longitudinal modes for a layered structure. Especially, we have shown how the ME response in the longitudinal mode can be easily deduced from the measured response in the transversal mode (and vice-versa). This paper is organized as follow. In section II, we present a model derived from the piezoelectric and piezomagnetic equations in a two dimensional quasi-static approach where demagnetizing corrections are accounted for each ME coupling mode (longitudinal and transversal), using the demagnetizing factor N. Useful tables of N values for discs or cylinders magnetized along radius or axis are available in the literature [START_REF] Chen | [END_REF]19 . For a given sample, the links between the axial and radial ME responses are studied theoretically. For the transversal ME coupling, the effect of a decrease in the magnetic layer thickness was also theoretically studied in term of demagnetizing effect and field penetration.

In section III, we present the fabrication method of The ME samples. (Ni 0.973 Co 0.027 ) 1-

x Zn x Fe 2 O 4 compositions, with x = 0, 0.125, 0.25, 0.5, have been synthesized by reactive Spark Plasma Sintering (SPS) method 20 . To the best of our knowledge, concerning layered ME composites, no publication in the literature concerns ferrites made by reactive SPS methods. However, this method permits high densification and an increase of the magnetostrictive properties can be expected. Zinc substitution has been used to help the sintering stage with SPS to be accomplished because of the high diffusion capability of the Zn 2+ ions. Moreover, as showed by some authors 7 , a certain amount of zinc permits to optimize the piezomagnetic behavior of ME composites. After SPS, all samples were annealed in natural atmosphere at 1000°C for re-oxidation, and some of them were quenched in air to estimate the effect of a heat treatment. All ferrite discs were pasted on commercially available PZT discs to form bilayers or trilayers and transversal ME coefficient measurements were performed at subresonant frequency (80Hz) .

In section IV, the ME responses of the ME samples made with ferrites with different Zn contents and heat treatments are presented. A possible explanation concerning the quenching effects is given. In this purpose, we have developed an original set-up to measure the intrinsic ME coefficients of ME samples. The aim of the measurement is to avoid the demagnetizing effect in the magnetic material when an AC magnetic field is applied. In the other hand, the link between the transversal and longitudinal ME modes is studied experimentally and theoretically in terms of demagnetizing effects and mechanical coupling. In the transversal mode, the demagnetizing effects in ME responses are also studied for samples including ferrite with various layer thicknesses and configurations. The mechanical coupling between ferrite and PZT layers is an important parameter that influence the ME response and it depends on the configurations of the layers. Studies were conducted on bilayers and trilayers to show what is the configuration with the best mechanical coupling. For a non-symmetrical sample, the possible effect of the flexural strain is bring out.

The performances of these ferrite/PZT bilayers have been assessed against other ME composites with high performances such as Terfenol-D/PZT bilayer. A Terfenol-D disc was purchased and pasted on a PZT disc. For relevant comparison, this ME sample exhibit the same geometry, dimension, and volume ratio, as our ferrite/PZT ME samples. The ME responses were explained estimating the piezomagnetic and elastic properties of both materials.

Finally, in section V, we report the fabrication of a passive current sensor prototype based on a transversal ME coupling. Layered ME samples made with NiCoZn-ferrites coupled with PZT exhibit a magnetic field sensitivity suitable to build non-resonant magnetic field or current sensors. It was characterized using square and triangle waveforms and it shows capabilities for high level AC current measurements ( ) in the kHz range with good accuracy.

II. Theoretical analysis.

In order to explain the behavior of a layered ME composite, we have first developed a quasistatic 2-dimensional model, with particular attention towards the demagnetizing effects in longitudinal as well as transversal coupling modes. The interface of the bilayer is in the (1,2) plane and we assumed a perfect mechanical coupling between the two phases. The external mechanical influences on the ME composite are considered negligible. The induced electric field is always in the (3) direction. Transversal ME coupling refers to the case whence DC bias and AC magnetic fields are both applied in the direction (1). Longitudinal coupling refers to bias and AC magnetic field applied in the direction (3) (see Fig. 1).

Transversal coupling.

The following constitutive equations are used for the direct and converse piezoelectric effects (Einstein summation convention):

(1) (2) where and are strain and stress tensor components, and are electric induction and electric field tensor components, and , , are zero field compliance, piezoelectric coefficient, and zero stress permittivity tensor components respectively.

In the same way, the magnetostrictive ferrite can be modeled as a piezomagnetic material, governed by the constitutive equations:

(3) (4) where and are strain and stress tensor components, and are internal magnetic field and internal magnetic induction (within the ferrite) tensor components, and , , are zero field compliance, piezomagnetic coefficient (which depends on the magnetic bias) , and zero stress permeability tensor components respectively.

In the bilayer configuration, the interface coincides with the 1-2 plane, and only extensional strain in those directions are considered. So only the , , , , , , , tensor components are to be considered. The electric field is produced in the direction (3) only, so and reduced to and . Lastly, assuming open electrical circuit (no current flowing from one electrode to the other), . So Eq. ( 1) and (2) reduce to:

(

In the same way, Eq. ( 3) reduces to:

(8) (9)
if the AC and DC magnetic field are applied along the direction (1).

At equilibrium, the force into the ferrite equates the one within the PZT (if we assume no forces absorbed by the glue layer), so from the stress point of view:

(10) (11)
where , is the volume fraction of PZT and is the volume fraction of ferrite.

Assuming ideal coupling at the interface, ferrite and PZT are equally strained, so equates with in one part, and equates with in the other part.

So, equating Eq. ( 5) with (8) on the one hand and Eq. ( 6) with (9) on the other, and writing the two expressions as a function of the stress within the PZT (using Eq. ( 10) and ( 11)), one obtains the formula:

Eq. (7) gives the electric field generated by the stress within the PZT:

Lastly, combining Eq. ( 12) and ( 13), the electric field is related to the AC internal magnetic field : (14) This formulation for the transversal coupling is similar to the one given by some authors 21 . But in Eq. ( 14) the induced electric field is related to the internal magnetic field.

Longitudinal coupling.

In this configuration Eq. ( 5), (6), and (7), governing the piezoelectric material behavior, remain unchanged. In Eq. ( 8) and ( 9), the direction of the internal magnetic field must be changed from direction (1) to direction (3) and consequently, the piezomagnetic coefficient is now:

(15) (16)
Lastly, the formula coupling the electric field and the AC internal magnetic field can be easily deduced from Eq. ( 14): (17) It must be noted that a flexural strain exists within an asymmetric bilayer, and it leads to a lowering of the extensional strain level. The model proposed here do not take into account the flexural behavior, and consequently the calculation may overestimate the ME response of a bilayer. Nevertheless, this model gives an overall trend of the mechanic, piezomagnetic, and piezoelectric parameter influences.

Demagnetizing effect.

Experimentally, the magnetoelectric effect is measured by applying to the ME sample a small AC magnetic field (produced by Helmholtz coils) superimposed to a DC field (produced by an electromagnet). The level of the applied AC field can be measured by means of a Hall effect probe or a search coil. Consequently, the ME coefficient is normalized using the applied magnetic field H a . In order to compare theory and experiments, theoretical formulas (Eq. ( 14) and ( 17)) must be expressed in term of the external field H a . The demagnetizing field created by the sample is opposed to the external applied field produced by the Helmholtz coils. Consequently the internal field is lower than the external one. Within the magnetic material, the internal magnetic field [START_REF] Liverts | [END_REF] (in average over the volume) is: (18) where N is the magnetometric demagnetizing factor ( ), and is the alternative magnetization variation produced by the small AC magnetic field. The alternative magnetization is related to the internal AC field: (19) Where is the reversible magnetic susceptibility (under constant stress). The internal AC field is expressed as: (20) χ can be considered constant for and practically independent of if .

In the same way, the bias DC field produced by the electromagnet is reduced by the demagnetizing effect in the ferrite. The internal DC field is given by: (

Where is the static magnetic susceptibility (under constant stress).

Consequently, the ME coefficient with respect to the external applied field, for the transversal coupling mode, , and for the longitudinal one, , are given by:

(22) (23)
Where , and are the radial and axial magnetometric demagnetizing factors respectively.

In the case of cylinders, the demagnetizing factors and depend on the ratio of thickness to diameter t/d of the magnetic sample and little on the susceptibility χ of the material. In Fig. 2, using data published by D. X. Chen et al., [START_REF] Chen | [END_REF]19 the radial and axial demagnetizing factors were plotted as function of t/d for different values of susceptibility. Good accuracy are obtained for demagnetizing factor and expressed as function of thickness to diameter ratio only. For a given piezoelectric material, mechanical, dielectric, and piezoelectric properties can be regarded as constants. So, the shape of the ME curves depend only on the intrinsic piezomagnetic coefficients and the static and reversible susceptibility which are controlled by the internal bias field . Note that the intrinsic piezomagnetic coefficients are related to strain derivatives with respect to the internal field H. According to Eq. (20), and ( 21) demagnetizing effects also influence the ME bilayers behavior.

Eq. ( 22) and ( 23) are quite similar. They differ only in the piezomagnetic coefficients and the demagnetizing factors. We can expect similar magnetoelectric behaviors when measurement are made in the transversal and longitudinal modes. Because Joules magnetostriction is a constant volume deformation (in general, volume magnetostriction can be neglected), for polycrystalline ferrite with random lattice orientations, the piezomagnetic coefficients are simply linked and it can be assumed that for the same internal bias field.

Theoretically, according to Eq. ( 22) and ( 23), high magnetoelectric effects are obtained when the piezomagnetic material has the following properties: (i) low reversible magnetic susceptibility χ which permits high internal AC field, (ii) high intrinsic piezomagnetic coefficient d, (iii) low compliance coefficients and . It is equivalent to maximize the following ratio:

. This ratio is quite similar to the magnetomechanical coupling factor 22 (where is the absolute permeability) which indicates the capabilities of a magnetostrictive material to convert magnetic energy to mechanical one (and vice-versa). In conclusion, good magnetic materials for magnetoelectric applications are to be chosen among the class of high magnetomechanical coupling piezomagnetic ferrite commonly used in ultrasonic transducer applications. In the 50'S and 60s, many investigations 11,12,13 have been made in the field of underwater acoustic. It turns out that cobalt substituted nickel ferrites have high magnetomechanical coupling factor, within the order of magnitude of 0.3 (at the optimum bias). These compositions will be the starting point for our study of ME bilayer.

III. Experiment.

Samples fabrication.

Nanosized (<50nm) powders purchased from Sigma-Aldricht (Fe 2 O 3 , NiO, Co 3 O 4 , ZnO) were used as precursor oxides. The compositions (Ni 0.973 Co 0.027 ) 1-x Zn x Fe 2 O 4 , where x = 0, 0.125, 0.25, 0.5, were obtained by mixing the different powders in appropriate ratios. All powders were mixed by ball milling (30 min at 200 rpm), and then grinded at 600 rpm for 1 hour. SPS was used for the spinel structure formation and sintering stages. Mixtures were loaded in a cylindrical graphite die (10mm inner diameter) between two pistons applying uniaxial stress. Carbon paper was used as separator between powder, carbon die and pistons. The reaction and then the sintering were carried out in neutral atmosphere (argon) by heating the powder with a pulsed DC current under application of uniaxial stress. The reaction stage was performed at 600°C under a pressure of 100MPa for 5 minutes. The densification is obtained at 850°C for 3 minutes under the same pressure. After sintering, the samples are obtained in the form of 10mm diameter and 2mm thick discs. For each composition, several samples were produced. All these samples were annealed in air at 1000°C for 1 hour. For each composition, we produced two samples: one quenched in air (except x=0) and the other slowly cooled (approximately 3.5°C/min). Part of ferrite discs (2mm thickness) were directly pasted with silver epoxy (Epotek E4110) on PZT discs (PZ27 (Ferroperm)) with the same diameter. One other part of ferrite discs were cut to reduce the thickness (1mm) and pasted on PZT discs (PZ27). Finally, two ferrite discs were drilled to form rings, and then, they were pasted on PZT rings (Pic255 (Physik Intrumente)). All the piezoelectric discs or rings are polarized in the thickness direction (3). The ME sample characteristics are resumed in Table 1. It must be noted that the SPS sintering process in argon atmosphere produces ferrites with some deficiency in oxygen, and some Fe 3+ ions reduce into Fe 2+ . The annealing at 1000°C in natural atmosphere do not re-oxidize the ferrite completely because of the low porosity. As a consequence, the conductivity of the material increases, but this is not affecting layered ME composites performances.

ME measurement procedure.

The ME coefficient is measured as a function of external applied DC magnetic field produced by an electromagnet 23 . For each working point, a small external applied AC magnetic field (1mT, 80Hz) produced by Helmholtz coils is superimposed. Low frequency is used to avoid any resonance effect, so ME bilayers are excited in quasi-static mode. The ME voltage is measured by means of a lock-in amplifier (EG&G Princeton Applied Research Model 5210) with high input impedance (100MΩ). All the measurement were performed at room temperature. When the external magnetic fields (AC and DC bias) are perpendicular to the electrical polarization direction, the experimental transversal ME coefficient is : (24) where is the electric field within the PZT layer. is the external AC field applied in the direction (1). When the magnetic fields (AC and DC bias) are parallel to the electric polarization direction, the experimental longitudinal ME coefficient is : (25) where is the external AC field applied in the direction (3).

IV. Results and discussion.

Influences of the quenching and Zn contents in the ferrites.

In order to measure the effects of heat treatment and Zn content on the properties of ferrites, the transversal ME coefficients were recorded for the different ferrite compositions (x= 0, 0.125, 0.25, and 0.5), for slow-cooled and quenched samples (see Fig. 3). The maximum ME effect occurs at magnetic DC fields between 30 kA/m and 55kA/m for all compositions. The maximum ME effect is obtained for x=0.125, and decreases with Zn content. For x=0.125, the ME effect is larger for the slow-cooled samples. By opposition, for x=0.25 and 0.5, the quenching enhances the ME coefficients. The increase in the non-magnetic Zn 2+ content from x=0.125 to x=0.5 produces two effects which work together: (i) the saturation magnetostriction decreases because of the dilution of the magnetostrictive cations (Ni 2+ , Co 2+ , Fe 2+ ), and so, the piezomagnetic coefficient decreases too; (ii) the permeability increase and as a consequence the internal field decreases according to Eq. (20). A possible explanation of the effect of heat treatment can be given as follow. CoFe 2 O 4 is usually considered as an inverse spinel ferrite, but the cations distribution depends on the heat treatment 24 . At high temperature, Co 2+ and Zn 2+ ions which have the same radius (82 pm) may be distributed in both sites (tetrahedral and octahedral) because magnetic interaction have no effect. By quenching, a part of Co 2+ cations can be frozen into their high temperature positions which correspond to a more randomized distribution 25 . By opposition, slow-cooling gives time for cations to move into their low temperature equilibrium positions. In contrast, for NiFe 2 O 4 ferrite, the cations distribution (inverse spinel) seems to be independent of the heat treatment or cooling method of the fabrication process 24 . In case of Co substituted NiZn-ferrites, a reasonable assumption is that the quenching affects the distribution of the Co 2+ cations in the tetrahedral and octahedral sites. This distribution is also influenced by the Zn 2+ rate: Zn 2+ cations which occupy the tetrahedral sites can affect the migration of Co 2+ cations during a thermal treatement. Thus, quenching and Zn 2+ rate affects the local electronic symmetry, and in turn, spin-orbit coupling dependent properties, namely the magneto-crystalline anisotropy and the magnetostriction.

Link between transversal and longitudinal modes.

To investigate the effects of the coupling modes, transversal and longitudinal ME coefficients were measured (see Fig. 4) for the sample # 0.5SC2/1. As expected, for longitudinal coupling, for which the AC and DC demagnetizing fields are higher, the peak of the ME curve is lower and it occurs at higher external bias field. Eq. ( 22) and (23) show that transversal and longitudinal ME coefficients are strongly linked and that they can be deduced from each other if demagnetizing field corrections are done, knowing the static and reversible magnetic susceptibility of the ferrite. For this purpose, a spherical sample of ferrite was machined (diameter: 2mm) and characterized using a Vibrating Sample Magnetometer (VSM) (LakeShore 7404). The virgin magnetization curve versus internal field (after demagnetizing field correction) is given Fig. 5. From this measurement, the differential susceptibility was deduced and plotted on the same figure. From transversal coupling to longitudinal coupling, due to the demagnetizing effects, the amplitude of the ME response must be corrected by the ratio . Obviously, at low magnetic bias, it is known that the reversible susceptibility is different from the differential susceptibility. But in this case, where both reversible and differential susceptibility are high, the ratio is independent of the susceptibilities and can be approximated by .The value of the susceptibility affects the result only if is within the order of 1 which practically means in the present case (or for H above 50kA/m). In this region (approach to saturation) the differential and reversible susceptibilities are equal. According to Eq. ( 20), ( 21), (22), and (23), the solid line curve in Fig. 4 is deduced from the experimental transversal coupling curve (dashed line), making demagnetizing field corrections. It is noted that for isotropic polycrystalline ferrites, in theory. Here, to fit the curves, we have taken piezomagnetic coefficients with a ratio of . This deviation can be explained by an anisotropic piezomagnetic behavior of the ferrite. This point will be discussed in section IV.5. of the paper. Concerning the transversal coupling, the peak of the ME coefficient is obtained for a external applied bias field. At this working point, the reversible susceptibility is around 23 and according Eq. ( 20), the internal AC field is four times lower than the external one. Hence, due to the demagnetizing field, the ME coefficient is correspondingly diminished.

Ferrite layer thickness effects on the ME response.

As seen before, radial and axial demagnetizing effects, which are quite different for a given sample, have a considerable influence on the ME response. The demagnetizing effect can be tuned in the same radial mode by changing the thickness of the magnetic material in the ME samples: according to Fig. 2, the radial demagnetizing factor decreases when the thickness is decreased for a given diameter. To illustrate this point, a ME bilayer sample was made with a thin ferrite disc of 1mm in thickness pasted on a 0.5mm PZ27 disc (sample #0.125SC1/0.5). Its behavior was compared to the reference ME sample with 2mm thick ferrite layer of the same composition pasted on a 1mm PZ27 disc (sample # 0.125SC2/1). Note that for better comparison, the two ME samples have the same PZT/ferrite volume ratio (γ=1/2). The two measured ME coefficients are given in Fig. 6. Both curves have approximately the same amplitude whereas the main effect of the demagnetizing field is to shift the peaks of the curves. The experimental ME curve of the reference sample (# 0.125SC2/1) was corrected in demagnetizing effect to obtain the behavior of the 1mm thick ferrite ME sample. The method used here is similar to the one used before for the longitudinal ME coefficient calculation: a spherical shape of ferrite was characterized using a VSM. From the virgin magnetization curve, the susceptibilities were deduced, and then demagnetization corrections were done. This theoretically corrected curve (thin dashed line in Fig. 6) exhibits correct downshift in the peak position but the ME amplitude is slightly overestimated with respect to the measured one. Next, a trilayer ferrite/PZT/ferrite of the same composition with 1mm thick for each ferrite layer pasted on a 1mm thick PZ27 layer was made (sample # 0.125SC1/1/1). Its ME coefficient (plotted in Fig. 6, thick dotted line) is quite higher than that of the reference bilayer sample. This behavior cannot be explained by a demagnetizing effect. In fact, the corrected curve in demagnetizing effect (thin dotted line) from that of the reference sample have quite lower amplitude compared to the experimental one. We assume that this high ME effect is due to a higher mechanical coupling between PZT and ferrite layers because the PZT layer is stressed on its two faces. Furthermore, due to the symmetric geometry of the trilayer, no flexural strain occurs: a higher stress is transmitted from the two ferrite layers to the piezoelectric one. In this case, the mechanical behavior of the ME composite is closer to the simplified model calculated in section II (see section IV. 5. for precisions) Note that for the trilayer sample, the horizontal shift in the ME curve is half less than the bilayer one. Whereas in the two cases the ferrite layers have the same thickness (1mm), in the trilayer case there is a magnetic coupling between the two ferrite layer, increasing the demagnetizing factor. We estimate that this factor is increased from 0.0881 for a single ferrite layer (1mm thick) to 0.115 for two ferrite layers separated by a 1mm PZT layer. To confirm the overall trend of a ME trilayer, one another sample (# 0.125SC0.5/0.5/0.5) was made: two ferrite layer (0.5 mm thick each) were pasted on both faces of a PZ27 layer (0.5mm thick). Its measured ME coefficient is plotted (dashed line) in Fig. 7. Due to a lower demagnetizing field and a good mechanical behavior, the peak ME coefficient is increased up to 0.55 V/A.

Effect of an inhomogeneous strain on the ME response.

The trilayer sample (# 0.125SC1/1/1) have quite higher ME coefficient compared to the bilayer reference sample (# 0.125SC2/1), and the whole difference cannot be explain if we consider only the demagnetizing effect. Firstly, we may assumed that a flexural strain of the bilayer produces a decrease of the stress in the piezoelectric layer compared of the case of a trilayer with no flexural strain. To answer this question, a trilayer sample was made: two PZ27 layers (0.5mm thick each) were pasted on both faces of a ferrite layer (2mm thick). This sample (# 0.125SC0.5/2/0.5) have the same demagnetizing factor and the same volume ratio as the reference sample. But due to its symmetric geometry, no flexural behavior can occur. The ME coefficient was measured and plotted in Fig. 7 (dotted-dashed line). This trilayer sample and the bilayer (reference) sample have comparable ME behavior with the same peak value of 0.2V/A. We can conclude that the flexural strain behavior of the reference bilayer sample have negligible influence on the peak of the ME coefficient since the whole thickness (3mm) is only 3.3 times lower than the diameter of the sample (10mm). Lastly, only the in-plane strain have to be considered to predict the ME response. The exact solution of the strain field (strongly inhomogeneous) in the whole ME sample can be calculated only by numerical methods (Finite Element Method, for example). Nevertheless, an experimental estimation of the strain level in each layers of the ME sample can be made. For this purpose, two strain gauges (EA-06-062TT-120, Micro-Measurements) were pasted on each free faces of the PZT and ferrites layers of the reference bilayer sample (# 0.125SC2/1). The strain gauges were chosen because of their small sensitive areas (1.8×1.8 mm 2 ) that permits local measurements near the edge of the faces where the strains are expected to be highly different. The longitudinal strains versus DC magnetic field are given in Fig. 8. As expected, the strain at the surface of ferrite layer is quite higher than the one measured for the PZT layer. At saturation, we obtain for the ferrite, and for the PZT. Although these measurements were made on surfaces, average values of the strains in each layers can be estimated when a linear profile for the strain along the direction (3) is assumed. Using geometric considerations, we obtain in the ferrite and in the PZT. The ratio of strains, at saturation, is quite low. In fact, the stress is applied on one face of the PTZ layer, the other face staying mechanically free. So, the propagation of a longitudinal strain from the ferrite/PZT interface to the free face of the PZT layer is mainly due to a shear stress effect. Note that the value of the ferrite strain at saturation ( ) of the ME sample is higher than the magnetostriction saturation ( ) measured for a mechanically free material (see Fig. 13). This difference can be explained as following: (i) the strain gauge was pasted near the edge of the ferrite disc of the ME sample while the magnetostriction measurement was done with a strain gauge centered on the surface of the disc where the strain is theoretically lower; (ii) the PZT layer acts like a mechanical load (or pre-load) on the ferrite layer, and as a consequence, the magnetostriction at saturation is increased in comparison to a mechanically free ferrite sample. The average strains in ferrite layer and PZT layer are quiet different: we have estimated and this effect highly deceases the ME response of a bilayer sample. So when the strain ratio is introduced for the longitudinal mechanical coupling, , as well as for the transversal mechanical coupling, with the same value , Eq. ( 22) is modified as (transversal ME coupling):

(26)
Obviously, an equivalent modification can be applied to Eq. ( 23) for the longitudinal ME coupling.

Effect of the quenching on the ME response.

For Zn-rich samples (x=0.25 and x=0.5), the quench of ferrites permits to enhance the magnetoelectric coupling. According Eq. ( 22), this enhancement can have two main causes: the improvement of the intrinsic piezomagnetic coefficients or a weakening of the magnetic susceptibility. To answer this question, the following experiments were made. For the composition with x=0.25 (quenched and slow-cooled), the ferrite discs were delaminated from the PZ27 layers. Then, they were drilled to form ferrite rings with a centered 3 mm hole. A thin PZT ring (PIC255, 10mm outer diameter, 5mm internal diameter, 0.25mm thickness) was pasted with silver epoxy on each ferrite rings. Samples are referenced 0.25Q2/0.25 and 0.25SC2/0.25. A 8 turns coil was wound on each ME ring. AC tangential magnetic field H AC (in the (1,2) plane) is forced within the ferrite when the AC current, I AC, is flowing into the coil:

, where D=6.5mm, is the mean diameter of the ferrite ring, and n=8, is the number of turns (so the demagnetizing factor N is 0 for H AC ). The top electrode of the PZT layers was separated into two parts (two strokes of file in the direction (1)) and then, the AC voltage produced by a half piezoelectric layer (parallel to the magnetic field) was measured by means of a lock-in amplifier. The ME samples were placed in a DC magnetic field applied in the direction (1) and produced by an electromagnet (see Fig. 9). The corresponding ME coefficients versus external applied field are given in Fig. 10. The two curves, for quenched ferrite sample and slow-cooled ferrite sample, are quite similar: the same maximum amplitudes are obtained for close DC fields (

). So the quench do not modify the intrinsic piezomagnetic behaviors of the ferrites. The differences obtained in ME curves for quenched and slowly cooled ferrite, when the ME coefficients are normalized using external applied AC field, are assumed to be the result of the demagnetizing effects. The initial permeability was measured for the two ferrites:

(quenched) and (slow-cooled) and it confirms that a less penetrating magnetic field in the second case reduces the ME coefficient according Eq. ( 22).

Co-substitued Ni-Zn ferrite properties compared to those of Terfenol-D.

In a aim of comparison, Terfenol-D discs with the same size as the NiCoZn-ferrites (10 mm diameter and 2 mm thickness) were purchased from Etrema. One of them was pasted on a Pz27 disc (10mm diameter, 1mm thickness) with silver epoxy. The measured transversal ME coefficient is plotted in Fig. 11 and compared to that of our best bilayer sample # 0.125SC2/1. As expected, Terfenol-D produces better ME effects but it is only 1.8 times higher. This good performance of the ferrite/PZT composite compared to the Terfenol-D one should be explained estimating the piezomagnetic and elastic properties of both materials. Magnetostriction curves (parallel and perpendicular to the H field in the (1,2) plane of the sample) were measured using a strain gauge (H06A-AC1-125-700, Micro-Measurements) pasted on a Terfenol-D disc.

is the magnetostriction measured in the direction (1) when an external field is applied in the direction (1).

is the magnetostriction measured in the direction (1) when an external field is applied in the direction (2). The result is given Fig. 12. One observes saturation magnetostriction as high as in the parallel mode and in the perpendicular one, and it is in the range of the data given by the manufacturer. At the optimal external bias field of the piezomagnetic coefficients are and . It should be also noted that, in this particular case, the piezomagnetic coefficients and are related to strain derivatives with respect to the external applied field H a , so the effects of the demagnetizing field is already contained in these measurements. In the same way, a strain gauge was pasted on a NiCoZn-ferrite (with x=0.125), and parallel and perpendicular in plane magnetostrictions were measured (see Fig. 13). The parallel magnetostriction saturation is which is approximately two times higher than the perpendicular one (

). One obtains the extrinsic piezomagnetic coefficients expressed as a derivative with respect to the external field: and at the optimal bias of . The and compliances were deduced from ultrasonic velocity measurements along the thickness direction of a NiCoZn-ferrite disc by using a pulse-echo technique (shear and longitudinal waves) at 20MHz. The longitudinal (

) and transverse (

) waves velocities yield: , and . Assuming perfect isotropic polycrystalline ferrite, and reduce to:

and . The Terfenol-D disc purchased from Etrema is grain oriented in the thickness direction and exhibit an axial symmetry. As a consequence, in the transverse direction, the compliances are rather high: and (data from Etrema and Dong et al. 10 ). So, we can say that the advantage due to the high piezomagnetic coefficient of Terfenol-D (17 times higher than the NiCoZn-ferrite one) is counter balanced by its high compliance (19 times higher than the NiCoZn-ferrite one). So according Eq. ( 22) , one can roughly estimate that Terfenol-D and NiCoZn-ferrite have ME performance within the same order when associated with PZT.

The magnetostriction characterization is a helpful tool to estimate the magnetomechanical anisotropy of samples. For the ferrite, the parallel saturation magnetostriction, , is two times higher (in amplitude) than . This leads to extrinsic piezomagnetic coefficients and in the same ratio, and consequently, the intrinsic piezomagnetic coefficients and have the same ratio. We can conclude to isotropic piezomagnetic behavior in the (1,2) plan. Measurement of saturation magnetostriction in the (1) direction, when a magnetic field is applied in the (3) direction, gives , which is 4 times lower than . It can be assumed that the value of the intrinsic piezomagnetic coefficients is roughly . As a consequence, the value of the ratio is -0.5 which is quite different from -1, the theoretical value for a perfect isotropic ferrite. So, we can conclude to large anisotropic behavior for 3-1 piezomagnetic coupling. The physical reason of this phenomenon is unclear, but we assumed that a preferred direction is induced when the uniaxial stress is applied in the (3) direction during the reactive and sintering stages of the SPS synthesis.

Using data of piezomagnetic, piezoelectric, and elastic properties (summarized in Table 2), theoretical ME coefficients in transversal coupling at optimal bias were theoretically calculated. For sample # 0.125SC2/1, the theory given by Eq. ( 22) predicts which is two times higher than the experimental one. Nevertheless, when a strain ratio of (as measured before) is introduced, the theory predicts (Eq. ( 26)) which is quite similar to obtained experimentally. In contrast, for a trilayer of the same composition (sample # 0.125SC1/1/1) we obtain experimentally which is closer to the theoretical value (corrected in demagnetizing field) given by Eq. (22) . Using Eq. ( 26), experiment and theory give the same result when a strain ratio of is introduced. At this point, it is clearly seen that a piezoelectric layer stressed on its both faces by two ferrite layers produces average strain 77.5% higher compared to the case of a PZT layer stressed only on one face by a single ferrite layer. Concerning the Terfenol-D/P27 bilayer, theory (Eq. ( 22)) leads to which is little bit more than twice higher than the experimental result. Here again, this discrepancy is assumed to be due to a low average strain ratio when the piezoelectric layer is stressed by a single magnetostrictive layer. Using Eq. ( 26), theory and experiment give the same result if a strain ratio of is introduced. This low strain ratio is assumed to be the result of the high stiffness of the Terfenol-D material.

From another point of view, the dynamic magnetostrictive properties of a material can be expressed in terms of energy conversion capabilities. The magnetomechanical coupling factor is a function of the intrinsic piezomagnetic coefficient , related to the internal field, . This later can be expressed using the extrinsic piezomagnetic coefficient and the magnetomechanical coupling factor become . Using data summarized in Table 2, calculations lead to for the NiCoZn ferrite, and for the Terfenol-D material which is roughly 2 times higher. It is interesting to see that the two ME coefficients of the two materials have the same ratio 2:1. This suggests that the magnetomechanical coupling factor is an appropriate criterion to select magnetostrictive materials to be used into ME multilayer composites.

V. Sensor prototype.

Lastly, we have made a prototype of a current sensor based on a ME composite. The trilayer ferrite/PZT/ferrite (sample # 0.125SC1/1/1) with was placed in a small ACcoil made with four turns of an isolated wire. The low bias field required to polarize the ferrite material is produced by two small permanent barium ferrite magnets. The distance between the magnets and the trilayer was set to obtain the highest ME effect. The AC current flowing into the AC-coil was produced by a power amplifier connected in series with a 4Ω power resistor. This current was sensing by a commercial active current probe (Tektronic A622) for comparison. The ME voltage was sensed directly by a passive voltage probe with 10MΩ input impedance connected to an oscilloscope (Lecroy Waverunner 44Xi). 10A peak square and triangle current waveforms at 1kHz were used to characterize the response of the ME sensor in the sub-resonant mode. Fig. 14 and Fig. 15 show that, at this frequency, the phase shift is negligible, and the sensor have a good linearity and low noise level. Here, the gain of the ME current sensor is approximately 87mV for 1A flowing into the wire. Obviously, this gain can be set to a given value by adding or removing some turns to the AC coil or by changing its size. We have already properly characterized current sensors with the same structure (but with lower sensibility). The results will be given in a paper [START_REF] Morin | A multiferroic composite based magnetic field sensor[END_REF] (not yet published).

VI. Conclusion

Co-substituted Ni-Zn ferrite were synthesized using a non conventional solid state reaction and sintering route based on a SPS method. These ferrites showing high magnetomechanical coupling factors are suitable to make multilayer ME composites exhibiting strong ME effects as predicted by a theoretical model. ME performances obtained with an optimized composition of NiCoZn-ferrite/PZT bilayer are comparable to those obtained with the same structure combining Terfenol-D and PZT. It was shown that the low piezomagnetic coupling performance of the ferrite (in comparison to the Terfenol-D) is balanced by a low compliance that permits high stresses produced by low strains. Another important parameter that influence the ME behavior is the demagnetizing factor associated with the susceptibility of the magnetic material. By lowering the internal AC and bias magnetic fields, demagnetizing effects partially shape the ME coefficient curves. By varying the thickness of the magnetic layer or by changing the exciting modes (axial or radial), the peak of a ME coefficient curve can be tuned, and its amplitude is affected. In the axial mode, due to better penetration of the magnetic field, the theory predicts higher ME coupling for low thickness to diameter ratios and as a consequence, the ME curve peak is shift down. In conclusion, the ME behavior of a layered ME sample is the result of three intrinsic parameters of the magnetic material: the intrinsic piezomagnetic coupling coefficients, the compliance, and the magnetic susceptibility. Furthermore, it was shown that the demagnetizing factor and the mechanical coupling between the layers are the extrinsic parameters of the magnetic material that influence the ME behavior. Finally, we used Co-substituted Ni-Zn ferrite associated with PZT in a trilayer structure as a ME current sensor. The device was purely passive: the bias field was obtained with two barium ferrite magnets and the ME voltage was directly measured with a passive voltage probe. The characterization in a nonresonant mode have shown a high linearity and a negligible phase shift. The gain of the sensor is closed to 90mV/A for courant in the 0-10A range that meets performance suitable in the field of power electronic applications. . Filled circles: . Open triangles: . Filled triangles: . Data are from D. X. Chen et al 16,[START_REF] Yang | PowerMEMS 2009[END_REF] . . Filled circles: . Open triangles: . Filled triangles: . Data are from D. X. Chen et al 16,[START_REF] Yang | PowerMEMS 2009[END_REF]

Fig 2 .

 2 Fig 2. Radial demagnetizing factor (triangle symbols) and axial demagnetizing factor (circle symbols) as a function of the thickness/diameter ratio of the magnetic material. Open circles:. Filled circles: . Open triangles:. Filled triangles: . Data are from D. X. Chen et al16,17 .

Fig 3 .

 3 Fig 3. Transversal magnetoelectric coefficient for the various Zn contents in ferrites. Top: slow-cooled ferrites. Bottom: quenched ferrites. All ferrites are pasted on PZ27 discs.

Fig 4 .

 4 Fig 4. Transversal (dashed line) and longitudinal (dotted line) magnetoelectric coefficients for the sample # 0.5SC2/1. The solid line is the longitudinal ME coefficient calculated from the transversal one.

Fig 5 .

 5 Fig 5. Magnetization and magnetization derivative measured for the slow-cooled ferrite with x=0.5 Zn content.

Fig 6 .Fig 7 .

 67 Fig 6. Transversal magnetoelectric coefficients for bilayers and trilayer made with NiCoZn ferrite (x=0.125) and PZ27. Thick lines correspond to experimental ME measurements. Thick solid line: 2mm/1mm ferrite/PZT bilayer (reference sample). Thick dashed line: 1mm/0.5mm ferrite/PZT bilayer. Thick dotted line: 1mm/1mm/1mm PZT/ferrite/PZT trilayer. The thin lines are curves deduced from the experimental one of the reference sample where demagnetizing effects were corrected. Thin dashed line: 1mm/0.5mm ferrite/PZT bilayer. Thin dotted line: 1mm/1mm/1mm PZT/ferrite/PZT trilayer.

Fig 8 :

 8 Fig 8: Strain curves versus applied external field along the parallel direction for the ME sample #0.125SC2/1 (reference sample). The closed circles correspond to strain measurement on the ferrite face, and open circles correspond to strain measurement on the PZT face. The magnetic field and strain measurements are parallel (and in the disc plane).

Fig 9 .

 9 Fig 9. Top view of the ME device when circumferential AC magnetic field is forced within the ferrite. The PZT top electrode is split into two half electrodes (in grey) which produce two opposite voltages V and V'. Only AC voltage produced by a half piezoelectric layer is measured.

Fig 10 .

 10 Fig 10. Transversal magnetoelectric coefficients when AC magnetic fields are forced within the ferrite. Solid line: sample # 0.25Q2/1 (quenched ferrite). Dashed line: sample # 0.25SC2/1 (slow cooled ferrite).

Fig 11 .

 11 Fig 11. Transversal magnetoelectric coefficient for sample # 0.125SC2/1 (solid line) and Terfenol-D/Pz27 2mm/1mm bilayer (dotted line).

Fig 12 .

 12 Fig 12. Magnetostriction curves versus applied external field along parallel (closed circles) and perpendicular (open circles) directions for a Terfenol-D disc. The magnetic field and strain measurements are in the disc plane.

Fig 13 .

 13 Fig 13. Magnetostriction curves versus applied external field along parallel (closed circles) and perpendicular (open circles) directions for a ferrite disc with x=0.125. The magnetic field and strain measurements are in the disc plane.

Fig 14 .

 14 Fig 14. Black line: voltage obtains with an commercial active current probe (gain: 100mV/A). Grey line: ME voltage obtains at the electrical output of the piezoelectric material. The current have a square waveform at 1kHz and 10A peak.

Fig 15 .

 15 Fig 15. Black line: voltage obtains with an commercial active current probe (gain: 100mV/A). Grey line: ME voltage obtains at the electrical output of the piezoelectric material. The current have a triangle waveform at 1kHz and 10A peak.

Fig 1 .

 1 Fig 1. Sketches of the transversal coupling (top) and longitudinal coupling (bottom). The 1-2 plane coincides with the bases of the cylindrical ME sample.

Fig 2 .

 2 Fig 2. Radial demagnetizing factor (triangle symbols) and axial demagnetizing factor (circle symbols) as a function of the thickness/diameter ratio of the magnetic material. Open circles:. Filled circles: . Open triangles: . Filled triangles: . Data are from D. X. Chen et al16,17 .

  Fig 2. Radial demagnetizing factor (triangle symbols) and axial demagnetizing factor (circle symbols) as a function of the thickness/diameter ratio of the magnetic material. Open circles:. Filled circles: . Open triangles: . Filled triangles: . Data are from D. X. Chen et al16,17 .

Fig 3 .

 3 Fig 3. Transversal magnetoelectric coefficient for the various Zn contents in ferrites. Top: slow-cooled ferrites. Bottom: quenched ferrites. All ferrites are pasted on PZ27 discs.

Fig 4 .

 4 Fig 4. Transversal (dashed line) and longitudinal (dotted line) magnetoelectric coefficients for (Ni 0.973 Co 0.027 ) 0.5 Zn 0.5 Fe 2 O 4 /Pz27 bilayer. The solid line is the longitudinal ME coefficient calculated from the transversal one.

Fig 5 .

 5 Fig 5. Magnetization and magnetization derivative measured for (Ni 0.973 Co 0.027 ) 0.5 Zn 0.5 Fe 2 O 4 slow-cooled ferrite.

Fig 6 .

 6 Fig 6. Transversal magnetoelectric coefficients for (Ni 0.973 Co 0.027 ) 0.875 Zn 0.125 Fe 2 O 4 /PZ27 bilayers and trilayer. Thick lines correspond to experimental ME measurements. Thick solid line: 1mm/2mm PZT/ferrite bilayer (reference sample). Thick dashed line: 0.5mm/1mm PZT/ferrite bilayer. Thick dotted line: 1mm/1mm/1mm PZT/ferrite/PZT trilayer. The thin lines are curves deduced from the experimental one of the reference sample where demagnetizing effects were corrected. Thin dashed line: 1mm/2mm PZT/ferrite bilayer. Thin dotted line: 1mm/1mm/1mm PZT/ferrite/PZT trilayer.

Fig 7 .

 7 Fig 7. Transversal magnetoelectric coefficients for (Ni 0.973 Co 0.027 ) 0.875 Zn 0.125 Fe 2 O 4 /PZ27 bilayers and trilayer.. Solid line: 1mm/2mm PZT/ferrite bilayer (reference sample). Dotteddashed line: 0.5mm/2mm/0.5mm PZT/ferrite/PZT trilayer. Dotted line: 1mm/1mm/1mm PZT/ferrite/PZT trilayer. Dashed line: 0.5mm/0.5mm/0.5mm ferrite/PZT/ferrite trilayer. All the lines correspond to experimental ME measurements.

Fig 8 :

 8 Fig 8: Strain curves versus applied external field along the parallel direction for the ME sample #0.125SC2/1 (reference sample). The closed circles correspond to strain measurement on the ferrite face, and open circles correspond to strain measurement on the PZT face. The magnetic field and strain measurements are parallel (and in the disc plane).

Fig 9 :

 9 Fig 9: Top view of the ME device when circumferential AC magnetic field is forced within the ferrite. The PZT top electrode is split into two half electrodes (in grey) which produce two opposite voltages V and V'. Only AC voltage produced by a half piezoelectric layer is measured.

Fig 10 .

 10 Fig 10. Transversal magnetoelectric coefficients for (Ni 0.973 Co 0.027 ) 0.75 Zn 0.25 Fe 2 O 4 /Pic255 bilayers when AC magnetic fields are forced within the ferrite. Solid line: quenched ferrite. Dashed line: slow cooled ferrite.

Fig 11 .

 11 Fig 11. Transversal magnetoelectric coefficient for (Ni 0.973 Co 0.027 ) 0.875 Zn 0.125 Fe 2 O 4 /Pz27 2mm/ 1mm bilayer (solid line) and Terfenol-D/Pz27 2mm/1mm bilayer (dotted line).

Fig 12 .

 12 Fig 12. Magnetostriction curves versus applied external field along parallel (closed circles) and perpendicular (open circles) directions for a Terfenol-D disc. The magnetic field and strain measurements are in the disc plane.

Fig 13 .

 13 Fig 13. Magnetostriction curves versus applied external field along parallel (closed circles) and perpendicular (open circles) directions for a ferrite disc with x=0.125. The magnetic field and strain measurements are in the disc plane.

Fig 14 .

 14 Fig 14. Black line: voltage obtains with an commercial active current probe (gain: 100mV/A). Grey line: ME voltage obtains at the electrical output of the piezoelectric material. The current have a square waveform at 1kHz and 10A peak.

Fig 15 .

 15 Fig 15. Black line: voltage obtains with an commercial active current probe (gain: 100mV/A). Grey line: ME voltage obtains at the electrical output of the piezoelectric material. The current have a triangle waveform at 1kHz and 10A peak.

Table 1 :

 1 Characteristics of the ME composite samples. The different ferrite compositions are (Ni 0.973 Co 0.027 ) 1-x Zn x Fe 2 O 4.

	Sample #	Ferrite Zn	Layer configurations	Layer thickness	Ferrite thermal
		content		(mm)	treatment
	0.5Q2/1	x=0.5	Ferrite/PZ27	2/1	quenched
	0.5SC2/1	x=0.5	Ferrite/PZ27	2/1	slow cooled
	0.25Q2/1	x=0.25	Ferrite/PZ27	2/1	quenched
	0.25SC2/1	x=0.25	Ferrite/PZ27	2/1	slow cooled
	0.125Q2/1	x=0.125	Ferrite/PZ27	2/1	quenched
	0.125SC2/1	x=0.125	Ferrite/PZ27	2/1	slow cooled
	0SC2/1	x=0	Ferrite/PZ27	2/1	slow cooled
	0.25Q2/0.25	x=0.25	Ferrite/Pic255	2/0.25	quenched
	0.25SC2/0.25	x=0.25	Ferrite/Pic255	2/0.25	slow cooled
	0.125SC1/0.5	x=0.125	Ferrite/PZ27	1/0.5	slow cooled
	0.125SC1/1/1	x=0.125	Ferrite/PZ27/Ferrite	1/1/1	slow cooled
	0.125SC0.5/0.5/0.5	X=0.125	Ferrite/PZ27/Ferrite	0.5/0.5/0.5	slow cooled
	0.125SC0.5/2/0.5	X=0.125	PZ27/Ferrite/PZ27	0.5/2/0.5	slow cooled

Table 2 :

 2 Material properties for PZ27 (cited from Ferroperm 26 ), Pic255 (cited from Physik Intrumente 27 ), NiCoZn Ferrite (x=0.125) , and Terfenol-D. Sketches of the transversal coupling (top) and longitudinal coupling (bottom). The 1-2 plane coincides with the bases of the cylindrical ME sample.

	FIGURE CAPTIONS
	Fig 1.


Sabrina Tartu
email: tartu@cebc.cnrs.fr

Aurélie Goutte

Paco Bustamante

Frédéric Angelier

Børge Moe

Céline Clément-Chastel

Claus Bech

Geir Wing Gabrielsen

Jan Ove Bustnes

Olivier Chastel

To breed or not to breed: endocrine response to mercury contamination by an arctic seabird

Keywords: Intermittent breeding, Mercury, GnRH challenge, Luteinizing Hormone, Blacklegged kittiwake

Mercury, a ubiquitous toxic element is known to alter expression of sex steroids and to impair reproduction across vertebrates but the mechanisms underlying these effects are not clearly identified.

We examined whether contamination by mercury predicts the probability to skip reproduction in black-legged kittiwakes (Rissa tridactyla) from Svalbard. We also manipulated the endocrine system to investigate the mechanism underlying this relationship. During the pre-laying period, we injected exogenous GnRH (gonadotropin-releasing hormone) to test the ability of the pituitary to release luteinizing hormone (LH, a key hormone for the release of sex steroids and hence breeding) in relation to mercury burden. Birds that skipped reproduction had significantly higher mercury concentration in blood than breeders. Endocrine profiles of these birds also varied based on breeding status (breeders vs. non-breeders), mercury contamination and sex. Specifically, in skippers (birds that did not breed), baseline LH decreased with increasing mercury concentration in males, while it increased in females.

GnRH-induced LH levels increased with increasing mercury concentration in both sexes. These results suggest that mercury contamination may disrupt GnRH input to the pituitary. Thus, high mercury concentration could affect the ability of long-lived birds to modulate their reproductive effort (skipping or breeding) according to ongoing environmental changes in the Arctic and impact population dynamics.

INTRODUCTION

Mercury is a ubiquitous toxic element of both natural and anthropogenic sources. In its methylated form, mercury can impair reproduction and disrupt the expression of estradiol and testosterone across vertebrates [1,2]. However the mechanisms underlying these effects are not clearly identified [3]. In response to increased day length, Gonadotropin Releasing Hormone (GnRH) is secreted and triggers luteinizing hormone (LH) release from the pituitary gland. LH, in concert with follicle-stimulating hormone (FSH), promotes gonadal maturation, sex steroid secretion and in turn, the onset of reproduction. It is conceivable that mercury acts primarily on the ability of the pituitary to secrete gonadotropin hormones (LH and FSH), altering sex steroids release and ultimately impairing reproductive behaviour. Mercury may also suppress GnRH in the hypothalamus, thereby reducing LH production. Clearly, there is a need for studies investigating the mechanisms of LH suppression by mercury [3] and subsequent repercussion in breeding animals.

Recent investigations have highlighted a major role for LH on skipped breeding behaviour (non-breeding by individuals that previously bred), a common feature in long-lived birds [4,5]. In some seabirds, skipping individuals show either low levels of baseline LH (Black-legged kittiwake, Rissa tridactyla [4]), or fail to maintain elevated LH levels after a GnRH injection (Snow petrel, Pagodroma nivea [5]). LH secretion also appears to be sensitive to environmental stressors in kittiwakes [4]. This opens the yet unexplored possibility that some endocrine disruptors like mercury may play a role in skipping behaviour, by altering the release and secretion of LH.

Here, we test whether mercury concentrations 1) are linked to skipping behaviour and 2) affect patterns of LH release during the pre-breeding period in an arctic population of Black-legged kittiwakes. To evaluate LH release, we challenged the pituitary with an exogenous injection of GnRH. Kittiwakes provide an excellent model to address these questions, as they bear elevated mercury levels in Svalbard [START_REF] Jaeger | Biomagnification of mercury in selected species from an Arctic marine food web in Svalbard[END_REF] and a significant proportion of adults skip breeding each year [4]. We predicted that high mercury concentration in blood would 1) be linked to a high probability to skip breeding 2) impair baseline and/or GnRHinduced LH levels.

METHODS

The study was conducted at Kongsfjorden, Svalbard (78°54′N, 12°13′E) from May 20 th to June 6 th 2008 (52 birds) and from May 21 st to June 7 th in 2011 (104 birds) during the pre-breeding period. Birds were caught on the nests and a blood sample was collected immediately after capture. In 2008, we performed a GnRH challenge (French veterinary services permit 79-2): immediately after the first blood sampling, kittiwakes were injected 0.1mL of a solution of GnRH (Electronic supplementary material, figure S1). Blood samples were collected from the alar veins 10 and 30 minutes after the GnRH injection to measure baseline and GnRH-induced levels of LH (both sexes) and testosterone (males only) as detailed in electronic supplementary material. Total mercury from all 2008 and 2011 samples was measured at LIENSs from lyophilized red blood cells, by atomic absorption spectrophotometry on 5-10 mg aliquots [START_REF] Bustamante | Total and organic Hg concentrations in cephalopods from the North Eastern Atlantic waters: Influence of geographical origin and feeding ecology[END_REF]. Mercury concentrations are expressed in µg/g dry weight. In both years, focal birds were measured as described in [4] to calculate a scaled mass index and observed daily. The nest content was checked every two days, to monitor if birds engaged in breeding (at least one egg laid) or if they skipped (no egg laid). We also monitored fitness, including date of first egg-laying, clutch size and the number of chicks that reached 12 days post-hatch (hereafter breeding success). To test the effects of mercury and scaled mass index on these reproductive parameters, we pooled data from 2008 and 2011 (no birds were sampled twice). Then, for 2008 we tested the effects of mercury concentration and interaction with sex, on baseline and GnRH-induced hormone levels in skipping and breeding birds. All statistical analyses were performed using R 2.13.1 and we used generalized linear models (GLM) with a normal/binomial error distribution and an identity/logit link function to test our biological assumptions. Model selection was performed by a step-down approach starting from the global model including all the independent variables.

RESULTS

Sex and year did not explain reproductive decisions (skippers vs. breeders; GLM, all p-values >0.10). Mercury predicted the likelihood to breed, as skippers had significantly elevated mercury levels compared to breeders (²= 14.06, p=0.001, Fig. 1A-B). This was true in both sexes (females: ²= 4.41, p=0.036; males: ²= 4.61, p=0.032). There was no interaction between mercury and either sex, year or scaled mass index (GLM, all p-values >0.87). Among birds that bred, pre-breeding mercury concentration did not predict first egglaying date, clutch size or breeding success (all p-values >0.18).

In birds that bred, baseline LH levels were higher in females than in males (F1,34=5.9, p=0.02), but were unrelated to mercury levels (F1,33=0.08, p=0.783; mercury × sex: F1,32=1.5, p=0.23, Fig. 1C-D). GnRH-induced LH levels were not linked to either sex (F1,17=3.23, p=0.09) or mercury levels (F1,17=0.88, p=0.361; mercury × sex: F1,17=2.72, p=0.118) in breeders.

In skipping birds, baseline LH levels were not affected by sex (F1,12=0.43, P=0.523) but significantly and negatively correlated to mercury levels in males, and positively in females (mercury × sex: F1,12=19, p<0.001; Fig. 1E-F). GnRH-induced LH levels significantly increased with increasing mercury concentration in skipping males and females (mercury: F1,10=21.6, p<0.001; mercury × sex: F1,8=0.07, p=0.805, Fig. 1E-F). Baseline testosterone levels tended to decrease in skipping males (F1,7=5.92, p=0.051) but not in breeding males (F1,19<0.01, p=0.97). GnRH-induced testosterone levels were not related to mercury levels neither in skipping (F1,5=0.1, p=0.761) nor in breeding males (F1, 9=0.6, p=0.458).

DISCUSSION

Long-lived seabirds often skip reproduction in certain years, and our previous investigations in kittiwakes demonstrate that LH levels are lower in the birds which choose to skip breeding (skippers, [4]). Could environmental toxicants influence LH and/or GnRH levels, and therefore reproductive decisions? We evaluated a possible role for mercury contamination in non-breeding black-legged kittiwakes, and investigated the endocrine mechanisms that underlie this decision.

As expected, total blood mercury measured after arrival significantly predicted the likelihood to breed. Although our study was correlational and would require experimental manipulation of contaminants [1,[START_REF] Hammerschmidt | Effects of Dietary Methylmercury on Reproduction of Fathead Minnows[END_REF], there is support for causal effects since experimental mercury administration can alter pairing in white ibises (Eudocimus albus) and suppress spawning in fathead minnows (Pimephales promelas) [1,[START_REF] Hammerschmidt | Effects of Dietary Methylmercury on Reproduction of Fathead Minnows[END_REF]. In our study, the most contaminated males and females were less likely to breed although there was a large overlap in mercury levels between skipping and breeding birds. Some of the skipping birds may be young or low quality individuals [5], and therefore be intrinsically more sensitive to mercury.

In birds that did breed, mercury had no effect on egg-laying dates, clutch size and breeding success. In breeders, total blood mercury averaged 1.8 µg/g (range: 0.91-3.08 µg/g) that could be below a threshold level beyond which breeding success is significantly impaired as shown in other bird species [START_REF] Evers | Adverse effects from environmental mercury loads on breeding common loons[END_REF]. However, mercury-breeding success relationships appear complex in birds since administration of a low mercury dose could even enhance breeding in Mallards Anas platyrhynchos [START_REF] Heinz | Enhanced reproduction in mallards fed a low level of methylmercury: An apparent case of hormesis[END_REF].

Mercury concentration predicted LH levels in skippers, but patterns were different among males and females, and varied between baseline and GnRH-induced LH. Baseline LH and testosterone decreased with increasing blood mercury concentration in males, as found in mercury-fed laboratory rats [START_REF] Ramalingam | Effect of mercuric chloride on circulating hormones in adult albino rats[END_REF]. Conversely, in skipping females, LH and mercury were positively related (although levels are still significantly lower than in breeding females [4]).

These data suggest that mercury-LH relationships are complex and LH disruption could also be the result of differential negative feedback from mercury given its estrogen-like effect [2].

To test the functionality of the pituitary, we performed GnRH challenges in breeders and skippers. Based on previous work [4], we assume that the dose of GnRH we used is sufficient to elicit a significant increase of LH 10 minutes after injection, and interpretation of our results is based on this assumption. If mercury is suppressing LH secretion directly at the pituitary, we would expect LH response to GnRH to be suppressed in skippers. Contrary to our predictions, skippers were clearly able to release LH, and increased LH 3-5-fold above baseline (breeders did showed a slight LH increase). Although based on correlations, it suggests that mercury may act at the hypothalamic level, disrupting GnRH synthesis or secretion. Evidence from other vertebrates demonstrates that mercury can accumulate in the hypothalamus and alter GnRH content and signalling [START_REF] Oliveira | Estradiol reduces cumulative mercury and associated disturbances in the hypothalamuspituitary axis of ovariectomized rats[END_REF]3]. In response to GnRH decline, the pituitary may have up-regulated GnRH receptors, explaining the large increase in LH with GnRH injection. Thus in kittiwakes, mercury contamination could lead to a decline in GnRH release, the subsequent increase of pituitary GnRH receptors explaining why the disrupted pituitary over-releases LH when experimentally challenged by GnRH. Although we originally hypothesized the mercury was targeting the pituitary, the induced LH response also points to a problem at the hypothalamus. It is additionally possible that mercury could bind to LH [START_REF] Laks | Luteinizing hormone provides a causal mechanism for mercury 194 associated disease[END_REF] making LH less able to activate gonadal receptors. Further experiments evaluating LH and GnRH expression in the brain would be necessary to meter out these possibilities.

Long-lived birds often skip breeding when foraging conditions are poor, modulating their reproductive effort according to environmental conditions [START_REF] Cubaynes | To Breed or Not to Breed: A Seabird's Response to Extreme Climatic Events[END_REF]. The present situation in the arctic is of concern: mercury levels in seabirds are increasing [START_REF] Mallory | Tracking contaminants in seabirds of Arctic Canada: Temporal and spatial insights[END_REF] and if combined to rapid climate change, we are facing a worst-case scenario [START_REF] Jenssen | Endocrine-Disrupting Chemicals and Climate Change: A Worst-Case Combination for Arctic Marine Mammals and Seabirds?[END_REF]. Ultimately, the likelihood to skip breeding may become too high to maintain current population levels.

Figure 1:

Pre-breeding mercury (µg/g dwt) and LH levels (ng/ml) in breeding and skipping black-legged Kittiwakes. Breeding birds (empty boxes) had lower mercury levels in blood than birds that would skip breeding (striped boxes), both in females (A) and males (B). Boxes represent median, 25 th and 75 th percentiles and outliers. In breeders (C-D), baseline and GnRH-induced LH levels were not affected by mercury. In skipping females (circles) baseline LH increased with increasing mercury (E), while in skipping males (triangles) baseline LH decreased with increasing mercury (F). GnRH-induced LH levels, in both skipping males and females, increased with increasing mercury levels (E-F).

GnRH challenge

Pre-breeding black-legged kittiwakes were caught on the nests and a first blood sample (ca. 0.3 mL) was collected within 3 minutes after capture. Immediately after this first blood sampling, birds were injected with 0.1 mL of a solution of GnRH ([Gin 8 ], Sigma Lot 121H04314) to test the responsiveness of the pituitary gland and the gonads. The GnRH was dissolved in physiological solution to yield a final dosage of 0.6 µg/0.1mL (1.5 µg/kg body mass in 1 mL of 0.9% saline solution). This dose of GnRH has been shown to be sufficient to elicit a significant increase of LH ten minutes after GnRH injection (Fig. S1-B) in several seabird species including black-legged kittiwakes [1,2,3]. We administered 0.1 mL of GnRH solution (GnRH-injected birds, N = 33) or saline solution (control birds, N = 21) directly into the alar vein. Kittiwakes were then placed into cloth bags and subsequent blood samples (ca. 0.3 mL) were collected from the alar vein at 10 minutes (to measure GnRH-induced release of LH in males and females) and 30 minutes (to measure GnRH-induced release of testosterone in males only) after the injection.

Molecular sexing and hormone assay

Blood samples were centrifuged, and plasma and red blood cells were separated and stored at -20°C until used respectively in hormone assays or molecular sexing, at the Centre d'Etudes Biologiques de Chizé (CEBC). Molecular sexing was performed as detailed in [2]. LH radioimmunoassay was conducted at the CEBC following the methods previously described and validated for Black-legged kittiwake plasma [1]. Pooled plasma samples of kittiwakes produced dose-response curves that paralleled the chicken LH standard curves ("AGM 51122F", sources: LH, Prf. Ishii and Wakabayashi, Wadesa University, Japan, Fig. S1).

Parallel curves indicate that the concentration-dependent binding of LH to antibody is similar in kittiwakes and chickens, and that this heterologous RIA can be used to assess relative levels of plasma LH in the Black-legged kittiwakes [1]. The lowest detectable concentration for LH was 0.06 ng/mL and the intra-assay coefficient of variation was 8.7 % (N = 3 duplicates). Plasma concentrations of testosterone were assayed for males only, by radioimmunoassay, at the CEBC as described in [3]. The lowest detectable concentration for testosterone was 0.05 ng/mL and the intra-assay coefficient of variation was 7 % (N = 3 duplicates).

Before GnRH-injection, baseline (i.e. at 0 minutes) hormone levels did not differ between GnRH-injected and control kittiwakes (GLM, LH: F1,51 = 0.04, p = 0.842; testosterone: F1,20 = 0.0045, p = 0.947, Fig. S1-A,B). Following GnRH injection, LH levels significantly increased over 10 minutes and then declined 30 minutes (GLMM, time as factor, F1,31 = 50.808, p <0.001, Fig. S1-B), without sex difference (sex: F1,31 = 0.857, p = 0.362; interaction: F1,30 = 1.738, p = 0.109). In control birds, LH levels did not significantly change over 10 and 30 minutes of handling (GLMM, F1,18 = 3.203, p = 0.09, Fig. S1-A) and were lower in males than in females at 30 minutes (GLM, F1,15 = 6.324, p = 0.024) but not at 10 minutes after the injection of saline solution (F1,16 = 2.239, p = 0.154). In GnRH-injected males, testosterone levels significantly increased over 30 minutes after injection (GLMM, F1,16 = 8.273, p = 0.011, Fig. S1-D), while in control males, testosterone significantly decreased over 30 minutes (GLMM, F1,12 = 11.341, p = 0.006, Fig. S1-C).

Figure S1 :

 S1 Figure S1: Hormonal change after the injection of the GnRH solution B and D panels (open

Figure S1 :

 S1 Figure S1: Hormonal change after the injection of the GnRH solution B and D panels (open

Norwegian Polar Research Institute, Fram center, NO-9296 Tromsø, Norway

Acknowledgments : This project was supported by Institut Polaire Français (IPEV project 330 to O. Chastel) and by Agence National de la Recherche (ANR project PolarTop to O. Chastel). The authors thank C. Breuner for useful comments, K. Sagerup, A. Fenstad, C. Trouvé and C. Churlaud for their great assistance in field and lab work.

Supplementary material

To breed or not to breed: endocrine response to mercury contamination by an arctic seabird