Stefan Hoerner
email: hoerner@ovgu.de

Shokoofeh Abbaszadeh

Thierry Maître

Olivier Cleynen

Dominique Thévenin

Characteristics of the fluid-structure interaction within Darrieus water

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Climate change and the greedy devour of our limited fossil resources since the beginning of the industrialization force us to change our global strategies of energy exploitation, heading towards renewable sources with sustainable technologies. Hydropower currently constitutes the largest share of renewable energies. Nevertheless, large dam systems, which provide high hydraulic head to improve the power density of hydropower systems, have a huge social and ecological impact, as reported very clearly by Rosenberg et al. [START_REF] Rosenberg | Environmental and social impacts of large scale hydroelectric development: who is listening?[END_REF], even if it is difficult to estimate the full range of this impact due to their complex far-reaching character [START_REF] Tilt | Social impacts of large dam projects: A comparison of international case studies and implications for best practice[END_REF]. In fact, even small-scale facilities obstruct fish migration. This issue is of recent research interest, bringing the need for theoretical performance considerations [START_REF] Peter | Upper limit for hydropower in an open-channel flow[END_REF][START_REF] Olivier Cleynen | Characterization of hydraulic power in free-stream installations[END_REF] as well as assessment of fish passability [START_REF] Basar | Rock-weir fishway I: flow regimes and hydraulic characteristics[END_REF][START_REF] Basar | Rock-weir fishway II: design evaluation and considerations[END_REF][START_REF] Müller | Numerical analysis of the compromise between power output and fish-friendliness in a vortex power plant[END_REF]. Hydrokinetic turbines directly convert the kinetic energy of the flow and allow for a move away from dams and towards operation in very low-head flow conditions. However, the available energy for a freestream installation is far lower as there is no potential energy which can be converted. Still, vertical-axis water turbines (VAWT), installed in marine currents and rivers could contribute to sustainable and environmentally -friendly hydropower exploitation. The most important advantage of VAWT is their area-based power density when used in farm configurations, which is reported to be significantly higher than for HAWT [START_REF] Robert W Whittlesey | Fish schooling as a basis for vertical axis wind turbine farm design[END_REF][START_REF] Dabiri | Potential order-ofmagnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays[END_REF][START_REF] Brownstein | Performance enhancement of downstream verticalaxis wind turbines[END_REF]. In sites with continuous flow directions, like rivers, a significant improvement of the rotor-based power coefficient can be achieved by collector constructions, as reported by Hashem and Mohamed for wind turbines [START_REF] Hashem | Aerodynamic performance enhancements of h-rotor darrieus wind turbine[END_REF]. The structure of a VAWT is quite simple, without need for guiding vanes or housing, but the flow conditions in the turbine are very complex: the blade angle of incidence α and relative speed w, resulting from the velocity trian-gle of free-stream velocity v ∞ and the tangential velocity of the blade ωR, vary constantly (fig. 1). Furthermore, VAWT blades operate under dynamic conditions including at least the onset of, or even deep dynamic stall. This is due to the high density of water, which requires a rotor with higher solidity σ compared to wind turbines. The consequences are smaller tip speed ratios λ and accordingly higher variations of the angle of incidence α in the best-efficiency point (BEP). For example, the turbine of the LEGI laboratory in Grenoble operates at σ = 1.1 and λ opt = 2 [START_REF] Maître | Modelling of the flow in a Darrieus water turbine: Wall grid refinement analysis and comparison with experiments[END_REF]; the turbine studied by Zeiner-Gundersen with σ = 0.9 and λ opt = 2.2 [START_REF] Herman Zeiner-Gundersen | A novel flexible foil vertical axis turbine for river, ocean and tidal applications[END_REF]. Those design points result in cyclic structural loads with small pulsing contributions to the thrust and multiple load peaks per turn. This is a general drawback of vertical-axis turbines and is known to cause damage due to material fatigue or defects on the main bearings [START_REF] Deglaire | Analytical solutions for a single blade in vertical axis turbine motion in twodimensions[END_REF][START_REF] Paraschivoiu | Wind Turbine Design: With Emphasis on Darrieus Concept[END_REF]. Only the sinusoidal component of the lift generates thrust (tangential force, see fig. 1). The cosine component is an order of magnitude higher and has to be compensated by the structure (normal force). The thrust-to-normal force ratio η = c T /c Nmax , similar to the lift-to-drag ratio in aerodynamics, is a measure of the quality of the configuration, with higher values being desirable. Extreme working conditions, such as low tip-speed ratios, tend to lower η.

Increasing the value of η requires control of the occurrence of flow separation, which is related to phenomena such as vibrations and flutter caused by the negative damping in light stall, or the abrupt loss of lift and increase of drag in deep dynamic stall. Dynamic stall was extensively investigated in the field of helicopter aerodynamics during the 1970s and 1980s by McCroskey [START_REF] Mccroskey | The phenomenon of dynamic stall[END_REF][START_REF] Mccroskey | Special Opportunities in Helicopter Aerodynamics[END_REF]. This work was adapted to VAWT -which work under comparable conditions, as their angle of incidence α varies periodically with respect to azimuth angle θ -by Laneville and Vittecoq [START_REF] Laneville | Dynamic stall: The case of the vertical axis wind turbine[END_REF], who experimentally investigated the forces on a VAWT operating under dynamic stall conditions. Other experimental studies of the complex flow conditions in VAWT use Particle Image Velocimetry (PIV) to visualize the flow field [START_REF] Fujisawa | Observations of dynamic stall on Darrieus wind turbine blades[END_REF]. Ferreira et al. [START_REF] Simão | Visualization by PIV of dynamic stall on a vertical axis wind turbine[END_REF] studied a one-bladed turbine at Re ≈ 100 000 with λ ranging from 2 to 4. In turn, Gorle et al. [START_REF] Gorle | PIV investigation of the flow across a Darrieus water turbine[END_REF] studied a four-bladed turbine in a towing tank in comparable conditions. Gorle showed that for a very common tip speed ratio of 2, the flow remained attached for an azimuth angle θ of 50°to 100°, while dynamic stall occurred from 120°to 220°. The flow progressively reattached from 240°o nwards, and a second vortex appeared between 0 and 40°(refer to fig. 1 for angles). Consequently, the flow was attached only 14 % of the time in these operating conditions.

One approach to control the forces variation and raise the efficiency is to use an active or passive pitch mechanism for the blades, in order to adapt α along the azimuth angle θ. Active techniques may also improve self-starting capabilities. A detailed overview of the state-of-technology and its opportunities is given in Pawsey [START_REF] Pawsey | Development and evaluation of passive variable-pitch vertical axis wind turbines[END_REF]. More recent studies mainly focused on decentralized actuator-based pitch [START_REF] Lazauskas | Modelling passive variable pitch cross flow hydrokinetic turbines to maximize performance and smooth operation[END_REF][START_REF] Zhang | Vertical axis wind turbine with individual active blade pitch control[END_REF][START_REF] Zhang | Effect of blade pitch angle on aerodynamic performance of straight-bladed vertical axis wind turbine[END_REF] and optimizing the pitch trajectory [START_REF] Thönnißen | A numerical analysis to evaluate betz's law for vertical axis wind turbines[END_REF].

The drawback of this approach is the mechanical or mechatronical complexity of the required system, which may need high maintenance efforts and is prone to failure.

Another approach to raise the single turbine efficiency is to optimize the blade shape. Recent studies show a possible improvement of more than 20 % which can be obtained compared to a commonly-used symmetrical NACA profile by the use of computational fluid dynamics coupled with an optimizer using genetic algorithms [START_REF] Ivanov | VAWT optimization using genetic algorithm and CST airfoil parameterization[END_REF][START_REF] Daróczy | Computational fluid dynamics based shape optimization of airfoil geometry for an Hrotor using a genetic algorithm[END_REF].

A third approach is to use an intelligent design featuring structural flexibility. It is known from bionic studies that whales raise the efficiency of their fins through flexibility [START_REF] Fish | Power output and propulsive efficiency of swiming bottlenose dolphins (tursiops truncatus)[END_REF]. Adjusted flexible structures can adapt to the flow by deformation. Flexible compound structures can naturally reproduce this effect by adapted stiffness which can be set by design. This was demonstrated experimentally and numerically by McPhee and Beyene, first for horizontal-axis wind turbines [START_REF] Macphee | Experimental and Fluid Structure Interaction analysis of a morphing wind turbine rotor[END_REF], later also for vertical-axis wind turbines through numerical analysis, with promising results [START_REF] Macphee | Fluid-structure Interaction analysis of a morphing vertical axis wind turbine[END_REF].

VAWT is a challenging task for numerical simulations. Reynolds-Averaged Navier-Stokes (RANS) simulations with fullymodeled turbulence and wall functions for the boundary layer can provide quite accurate power predictions in the turbine bestpoint [START_REF] Maître | Modelling of the flow in a Darrieus water turbine: Wall grid refinement analysis and comparison with experiments[END_REF] and show good accordance for the forces integrated over the whole blade [START_REF] Ferreira | Simulating Dynamic Stall in a 2D VAWT: Modeling strategy, verification and validation with Particle Image Velocimetry data[END_REF], but have strong dependency of the chosen turbulence model and grid refinement [START_REF] Daróczy | Comparative analysis of turbulence models for the aerodynamic simulation of H-Darrieus rotors[END_REF] while the shear stress transport k-ω model is considered to be most suitable for VAWT [START_REF] Gorle | Flow and performance analysis of H-Darrieus hydroturbine in a confined flow: A computational and experimental study[END_REF]. They may fail at low λ when deep dynamic stall is the governing flow regime. They are also known to badly reproduce key aspects of the flow field, in particular boundary layer separation [START_REF] Ferreira | Simulating Dynamic Stall in a 2D VAWT: Modeling strategy, verification and validation with Particle Image Velocimetry data[END_REF][START_REF] Daróczy | Correlation of the power coefficients of H-darrieus wind turbines obtained using different turbulence models in CFD computations[END_REF][START_REF] Daróczy | Comparative analysis of turbulence models for the aerodynamic simulation of H-Darrieus rotors[END_REF]. Separation is often overestimated and the point of occurrence shifted in time (and so in θ). RANS-based, two-way strongly-coupled simulations of the fluidstructure interaction (FSI) on highly deformable VAWT structures might capture these high dynamic flow conditions. However, they may not always provide very reliable results, since the position of the separation point and the load (pressure) distribution on the blade both strongly influence the behavior of such flexible structures. Threedimensional Large-Eddy Simulations (LES) or Detached-Eddy Simulations (DES) appear to be significantly more accurate, but remain computationally extremely challenging [START_REF] Ferreira | Airfoil optimization for stall regulated vertical axis wind turbines[END_REF][START_REF] Patil | Large eddy simulation of an H-darrieus rotor[END_REF]. Such simulations are almost impossible on current supercomputers when two-way FSI is involved and the algorithm enters, for each time step, an internal loop for structure deformation versus flow pressure distribution [START_REF] Tukovic | Open-FOAM library for fluid structure interaction[END_REF]. Another issue is the mesh deformation, which can be challenging at the fine mesh resolutions required for LES.

This explains the necessity of further experimental investigations, as an essential source of information. Zeiner-Gundersen presented an experimental study with deformable blades on a 5-bladed low-λ VAWT with promising results [START_REF] Herman Zeiner-Gundersen | A novel flexible foil vertical axis turbine for river, ocean and tidal applications[END_REF]. The flexibility improved self-starting capabilities, raised the efficiency, and shifted the BEP to lower values of λ. One last advantage is the in-crease in fish-friendliness of the device associated with lower rotational speeds [START_REF] Müller | Numerical analysis of the compromise between power output and fish-friendliness in a vortex power plant[END_REF].

The objective of the present study is to experimentally investigate the two central questions: Can flexible structures 1) lower the cyclic structural load, and 2) perhaps even improve the efficiency of vertical-axis water turbines?

Modeling

In order to simplify the experimental setup for the study, the VAWT is replaced by a surrogate model, which allows to precisely study the influence of structure flexibility concerning the occurrence of dynamic stall. This is the dominant issue for working points at low λ, which are particularly interesting for VAWT with low ecological impact. All secondary effects like tip and strut effects or blade-blade interaction, which become important at higher λ [START_REF] Daróczy | Comparative analysis of turbulence models for the aerodynamic simulation of H-Darrieus rotors[END_REF], are neglected.

The two targets of the study -lifetime and efficiency-are quantified using the maximum normal force (non-dimensionalized as the average amplitude of normal coefficient ĉN ), the thrust efficiency η, and the tangential force (non-dimensionalized as the thrust coefficient c T ).

The amplitudes of the cyclic loads (normal force) are a crucial factor for the turbine lifetime. High-cycle fatigue analysis based on S -N diagrams relates the number of cycles before fatigue failure N to magnitude S of the stress peaks. In such an analysis, it is known that N increases exponentially when S is lowered [START_REF] Castillo | A Unified Sta-tistical Methodology for Modeling Fatigue Damage[END_REF]. The amplitude of the normal coefficient (ĉ N ) (see eq. 9) can be seen as an equivalent, as S is proportional to it.

The tangential force delivers the turbine torque and serves to compare the benefit of different levels of flexibility for a given turbine design and operating point (eq. 7). The thrust-to-normal force ratio η is a benefit-tocost ratio in this study.

For the surrogate model, a single-bladed VAWT is considered as an oscillating hydrofoil (fig. 2). This concept was used al- in other studies such as that of Ly et al. [START_REF] Ly | Experiments on an oscillating aerofoil and applications to wind-energy converters[END_REF]. As a consequence of this approach, some characteristics of real VAWT are not taken into account. Strut and tip losses, as well as blade-blade interaction, are not present. The model does not reproduce the upstream-downstream and blade-wake interactions. Therefore, values for thrust are expected to be raised artificially, especially in the downstream part of the path. Further quantitative studies will have to take those complex flow characteristics into account.

Also, in the present case, the flow velocity w, which is alternating in real turbines, must be kept constant in the closed-loop water channel used for this study. This will result in a constant Reynolds number. However, McCroskey showed that the influence of Re is small for a fully turbulent flow. This was also true for the normal force and the vortex shedding [START_REF] Mccroskey | Dynamic stall experiments on oscillating airfoils[END_REF].

A dominant factor to determine the flow conditions on the blade is the tip speed ratio λ. It is defined as the ratio of blade tangential speed ω D R to free-stream speed v ∞ :

λ = ω D R v ∞ (1)
Eqs.2-4 below describe the motion and the flow for such a blade. Using λ and the rotor's azimuth angle θ, the angle of incidence α follows a trajectory for the non-sinusoidal oscillation of a blade (fig. 3) that is given by:

α = arctan sin θ λ + cos θ (2)
Then, as shown by Laneville et al. [START_REF] Laneville | Dynamic stall: The case of the vertical axis wind turbine[END_REF], the angular velocity α of the pitch motion can be calculated with respect to the angular velocity of the turbine ω D , λ and θ:

α = ω D (1 + λ • cos θ) 1 + 2λ • cos θ + λ 2 (3)
The alternating relative flow speed on the blade of a VAWT w is obtained with eq. ( 4) and depends on v ∞ , λ and θ:

w = v ∞ 1 + 2λ cos θ + λ 2 (4)
In order to transfer this approach into an oscillating airfoil experiment in a closed water tunnel, the inlet speed becomes the relative flow speed and is set constant. Therefore, the root mean square (RMS) of the relative flow speed along one turn of the rotor is set as v ch for the channel in the experiment. It corresponds to the average inlet speed and is given by volume flow rate divided by the channel cross-section. The thrust coefficient c T , the normal force coefficient c N (and its amplitude ĉN ) can be calculated from c L and c D (fig. 4):

c D = F D 0.5 • ρ • s • v 2 ch (5) c L = F L 0.5 • ρ • s • v 2 ch (6) c T = c L • sin α -c D • cos α (7) c N = c L • cos α + c D • sin α (8) ĉN = c Nmax -c N min 2 (9)
Those coefficients will allow to compare the experimental results of the flexible hydrofoils with those of the rigid foil reference (see section 3). The flow regime on the blades depends strongly on λ and on the solidity σ of the turbine. The definition of σ is not uniform in literature; it is often based on the diameter, but sometimes on the radius. In line with former studies at the LEGI laboratories, a convention conformal to [START_REF] Maître | Modelling of the flow in a Darrieus water turbine: Wall grid refinement analysis and comparison with experiments[END_REF] is used: the solidity is then defined as the ratio of the plan view area of the blades to half of the turbine's cross-section area:

F y (lift) α F x (drag) F' y (normal force) F' x (thrust) V ch
σ = n • C R (10)
These two parameters can be combined into a non-dimensional number, the reduced frequency k D , which determines the stall behavior of the flow in a VAWT. It relates the ratio of the time scale of the vortex convection over a profile to the time scale of the profile motion. Starting with k, from helicopter aerodynamics [START_REF] Mccroskey | The phenomenon of dynamic stall[END_REF] (eq.( 11), left), then specifically for a blade in a rotating reference frame [START_REF] Laneville | Dynamic stall: The case of the vertical axis wind turbine[END_REF] (eq.( 11), right), the reduced frequency k D for a VAWT is given by eq.( 12) from Laneville and Vittecoq [START_REF] Laneville | Dynamic stall: The case of the vertical axis wind turbine[END_REF]. In the case of a non-symmetric motion trajectory, α is the absolute pitch speed. That is the reason for λ -1 instead of 1 -λ in the denominator of eq. ( 12) which leads to positive k D even if αmax is in the descending pitch motion (fig. 3).

k = C • αmax 2v ∞ • α max = C • αmax ω D • 2R • α max (11)
k D = C 2 • R • (λ -1) • arctan (λ 2 -1) -1 2 (12)
The rotor frequency is given by the angular velocity ω D (eq. (13 left). Considering now the case of an oscillating profile in a tunnel, the average oscillation frequency f o can be calculated from the oscillation period T osc (eq.(13 right) which connects the turbine rotation to the profile oscillation:

f D = ω D /2π = f o = 1 T osc (13)
However, the angular velocity α of the profile is not constant. In this case f o alone is not sufficient to characterize flow dynamics from the forced oscillation. Therefore, the reduced oscillation frequency k o is more adequate. k o is introduced inserting eq.( 2) and eq.( 3) into eq.( 11)-right, which leads to eq.( 14):

k o = π • f o • C v ch • (λ -1) • arctan (λ 2 -1) -1 2 (14)
This formulation of k o accounts for the nonsinusoidal shape of the evolution of α with respect to time. The sawtooth-like curve depends on the value of λ (see eq.( 2)) and has a very strong influence on the unsteady effects characterizing the flow. In both equations 12 and 14, the case of λ=1 leads to a singularity with infinite k (fig. 5), as α jumps from 90°to -90°at θ = π (see eq.( 2)):

McCroskey showed that the reduced frequency is a crucial parameter for the stall dynamics. A NACA0012 behaves at k=0.004 almost quasi-static, while the characteristics corresponds to dynamic stall at k=0.06 upwards [START_REF] Mccroskey | The phenomenon of dynamic stall[END_REF]. These characteristics depend on the maximum angle, as well as the foil geometry. For the given experimental setup, the quasi-static characteristics were found for k o <0.01 and the fully dynamic state was reached for all sets at k o =0.06.

The parameter k D includes the ratio of chord length C to the turbine radius R and links it to the tip speed ratio λ. The latter defines the operating point of the turbine. The oscillation frequency f o substitutes R in k o . This allows to cover an entire field of turbine designs by the variation of only two parameters: 1) the reduced frequency k o and 2) the tip speed ratio λ. Their influence is mapped in fig. 5. This feature will be used in the experiments to cover the range relevant for most common VAWT designs.

Experimental Setup

A set of NACA0018 hydrofoils is investigated in the study: three flexible variants are investigated, along with a fully-rigid milled aluminum foil for reference. The flexible foils consist of a milled aluminum leading edge, in which a carbon composite blade is inserted along the length of the foil (fig. 2). Three values for the blade thickness t are investigated: 0.3, 0.5 and 0.7 mm. The stiffness of the foil grows with t 3 , since the second moment of inertia I reads:

I = b • t 3 12 ( 15
)
The silicone embodiment has a Young's modulus 1.5 × 10 5 times smaller than that of the carbon composite, so its contribution to the overall stiffness is neglected. Structural effects like strain hardening of silicone polymers under cyclic loads with high frequency, as well as the influence of the blade natural frequency and damping, are the subject of ongoing investigations by the authors and are neglected in this first work. Each foil is placed in a closed-loop water channel at LEGI Grenoble (fig. 2). A forced rotational oscillation is generated with a 5 kW servo drive system, following the trajectory defined by eq.( 2). Hydrodynamic forces produce large deformations of magnitude 25 mm for a foil with 66 mm chord length (fig. 6). They are measured with a fully-submerged, six-axes load cell underneath a base plate on which the hydrofoil is mounted. The sensor rotates along with the foil leading edge. The pivot point is placed at quarter chord (fig. 7). The rotated six-axes load-cell provides thrust and normal force. Then, a transformation matrix R Z (α) is applied to project the forces and the torque to the static (earth) reference frame and to obtain lift and drag:

(F, T) xyz = R Z (α) × (F', T') xyz (16) with R Z (α) =   cos α sin α 0 -sin α cos α 0 0 0 1   ( 17
)
The experimental parameters for the setup were chosen in order to achieve results comparable with those from previous studies on a VAWT model at LEGI [START_REF] Maître | Modelling of the flow in a Darrieus water turbine: Wall grid refinement analysis and comparison with experiments[END_REF]. This VAWT model is subsequently called LEGI turbine:

Geometrical similarity:

The LEGI turbine is built with 4% cambered NACA4518 alike hydrofoils. These follow the flow curvature of the rotational motion of the turbine blades [START_REF] Amet | 2D numerical simulations of bladevortex interaction in a Darrieus turbine[END_REF]. In the present experiment they are replaced by a symmetric NACA0018, since the flow in the channel has no rotational component.

Reduced frequency:

The range of tip speed ratio was set to λ = [START_REF] Basar | Rock-weir fishway I: flow regimes and hydraulic characteristics[END_REF][START_REF] Basar | Rock-weir fishway II: design evaluation and considerations[END_REF]. This leads to angles of attack α max = [20°, 30°]. The resulting reduced frequency for the LEGI turbine varies between k D = 0.26 at λ = 3 and k D = 0.35 for λ = 2 [START_REF] Maître | Modelling of the flow in a Darrieus water turbine: Wall grid refinement analysis and comparison with experiments[END_REF]. Due to sensor stiffness, the maximum frequency that could be achieved in the present study was f o = 6.45 Hz. Higher frequencies would lead to sensor damage through resonance. This limited the maximum achievable range to k o = 0.71 for λ = 2 and k o = 0.653 for λ = 3 (see fig. 5).

Chord-based Reynolds number:

Re is a function of the azimuth angle θ for VAWT, the (fixed) experimental Reynolds number was chosen to correspond to the RMS(Re) along one revolution (Re=200 000). A flow speed of v ch = 3.5 m s -1 in the water channel leads to a profile chord length C = 0.066 m. For the flexible foil (t=3 mm) case (inlet velocity was set 3.0 m s -1 ) the variations remain below 1% of the average velocity and are considered negligible. v ch is measured with the forces/moments for each data point at 1 kHz acquisition rate. k o was calculated using the average value of v ch for each period and than averaged.

Confinement:

The maximum blockage ratio can reach up to 12 % (for the rigid foil, at a maximum angle α max = 30°). This value exceeds 6%, which is considered a safe limit for a negligible influence [START_REF] West | The effects of tunnel blockage and aspect ratio on the mean flow past a circular cylinder with reynolds numbers between 10 4 and 10 5[END_REF]. However, confinement results in higher lift forces. On flexible foils, the deformation of the blade tends to decrease blockage for high angles of incidence (as can be seen in fig. 6).

Measurement equipment, filtering and uncertainty:

All experiments have been repeated twice in an independent manner, with no notice-able differences. In consequence any remaining measurement errors are considered to be systematic.

The experiment is controlled with a purpose-built Python-based environment. To achieve accurate set point control, an Ethernet-based communication with the drive system was implemented using the Telnet protocol. The implemented algorithms allow to perform arbitrary periodical motion for a given trajectory.

A low-cost acquisition card (labjack T7 pro) collects and streams the data with 1 kHz sample rate at 16 bit accuracy for volume flow rate, temperature, three forces, three moments, position feedback and an external trigger signal.

The data is filtered with a hardware-based R/C filter with a 480 Hz low pass, to prevent aliasing and to eliminate noise from the power inverter. No further filtering or signal software-based postprocessing was necessary.

The set point precision of the drive system is given with 0.058°(by 0.0439°resolver resolution, as the zero angle was set with 0.014°accuracy 0.25 mm m -1 with a water level).

Standard weights were used to determine the static accuracy of the load-cell-based force measurement system. The maximum error was found to be less than 0.009 % to full scale (800 N) and from 0.05 % to 4.8 % relative error when calibrating with loads from 2 kg to 0.1 kg mass load. In consequence the static load uncertainty is considered negligible for a single-axis load in the range of the experiment with -200 N < F y < 200 N and 0 N < F x < 100 N.

However, significant crosstalk is specified by the manufacturer: from 0.3% of full scale 800 N (y to x and conversely) to 1.82 % of 1600 N (for z to x). Also, the dynamic characteristics of the sensor (0.26 % hysteresis on full scale of 800 N for x and y) raise the uncertainty. In summary, the signal for the dynamic drag measurements without profile stall has to be taken in the range of the uncertainty.

In a second step, the static lift and drag coefficients for the system were captured with and without water; the results of the difference between them -the hydrodynamic forces-for the rigid hydrofoil were compared to computed results produced with the JavaFoil utility [START_REF] Hepperle | JavaFoil -Analysis of Airfoils[END_REF]; the results are displayed in fig. 8. Measurements and calculations are consistent below the static stall angle. However the slope of the experimental lift curve is less steep and the drag curve is shifted to lower magnitudes. The differences remain <1% of the sensor full scale and the effect on the drag can be explained by the sensor crosstalk.

Since JavaFoil is not able to predict accurate results in the stall region, no lift and drag coefficients were computed there.

Table 1 will give an overview of the experimental parameter:

Results

The experiment begins with a quasistatic/transitional low-frequency case of f o = 0.22 Hz. The frequency is then raised in seven steps up to 5.71 Hz for λ=2. For λ=3, eight steps were performed up to a fre- Similar trends are observed for both rigid and flexible foils in the second half of T. Compared to the first half of the motion, the magnitude of both c L = and c D is increased, as is the stall angle. This is due to the different motion α (quantified by eq. 3 and visible in fig. 3 and as the slope of the black curve in figs. 9-10). Rigid hydrofoil: With this increase in k o , the stall angle is raised very significantly (α stall = 27°, c Lmax 2.7). Past this angle, the loss of lift is less pronounced than for lower k o ; however, a hysteresis loop becomes visible and the flow does not seem to reattach before the shift in direction. At zerocrossing, c L already takes the value -1.5. The point of no lift α zl is reached at α zl =12°i n the descending and α zl =-10°in the ascending motion. Thus, the lift trajectory is shifted leftwards with respect to α. In the meantime, the integral of the lift for one period increases.

The drag curve also changes significantly: the characteristic spike with onset of stall disappears, while the two maxima are increased and display a slender shape. The hysteresis concerning lift does not appear for drag. The drag coefficient peaks at 1.0 in the descending branch (at α= 27°) and at 1.5 in the ascending branch (at α= -28.5°).

Flexible hydrofoils: All flexible foils display less lift than the rigid foil. The integral of the lift over the trajectory is lower and it decreases together with the stiffness. The stall angle is increased, with the most flexible foil (t=0.3) achieving c Lmax. =2 at α stall =29°. The drag curves display similar behavior to those of the rigid foil. Nevertheless, the drag is everywhere lower, and the maxima are re-duced by 25 to 50 % compared to those of the rigid foil. For all foils, for both lift and drag, some weak oscillations begin to appear. Rigid hydrofoil: As the reduced frequency is increased, the stall angle increases to reach α stall =29°. However, the lift coefficient never exceeds c Lmax =2.7. Peaks in the drag coefficients which were observed at lower frequencies diminish.

Flexible hydrofoils: All three foils follow the trend described above. The two most rigid foils (t=0.5 and 0.7 mm) have lift Larger high-frequency oscillations are now observed for all curves and all foils. It is possible that the natural frequency of the multi-mass system containing the sensor, the base plate and the hydrofoil (fig. 7), is approached. A light dynamic stall with negative damping [START_REF] Mccroskey | Special Opportunities in Helicopter Aerodynamics[END_REF] may also play a role. Those effects are under further investigation, requiring deeper knowledge of the structural properties and especially of the flow field.

Rigid hydrofoil: There are only light indications of stall, in the descending branch, with c Lmax =2.5 at α stall = 30°. Compared to the previous (lower) frequency, the maximum drag is significantly reduced.

Flexible hydrofoils: As for the rigid foil, stall indicators become less dominant. The loss of lift and the overshoot of drag are shifted to higher azimuth angle, while the hysteresis loop becomes narrower. Lower values are favorable, since lifetime rises exponentially with diminishing stress; A second-order polynomial curve fit of the data was added. These results correspond to λ=2 for four NACA0018 hydrofoils: one rigid and three flexible foils with different blade thicknesses: [0.3, 0.5, 0.7] mm.

Performance and lifetime improvements

The relationship between reduced frequency and thrust coefficient is shown in fig. 11(left). It displays the average thrust coefficient for one rotor revolution as a function of reduced frequency. It can be seen that the most flexible hydrofoil performs best, with significant improvement compared to the rigid reference especially in lowk o region. The effect becomes less important with higher k o . A maximum could not be obtained for these curves, maybe due to the experimental limitations on the oscillation frequency. The model allows to examine the effect of flexibility in specific design points, one for each k o . The comparison between two k o or design points is not possible in this model. In this case, the power output c P would have to include the turbine radius (which grows with raising k o as the chord length is constant) and further parameters like secondary effects as tip losses or bladeblade interaction, which is not possible with the current measurements. For k o =0.71, the intermediate flexible foil (t=0.5 mm) overperforms the most flexible one (t=0.3 mm). This indicates that the optimal stiffness is related to k o , but demands further investigations. The LEGI turbine model with BEP at λ=2 has a σ=1.1 and so a value of k D =0.35 [START_REF] Maître | Modelling of the flow in a Darrieus water turbine: Wall grid refinement analysis and comparison with experiments[END_REF]. At this operating point (k o =0.35), the most flexible hydrofoil (t=0.3 mm) provides best performance with 20% improvement of thrust compared to the rigid reference.

The influence of foil stiffness on the turbine lifetime is displayed in fig. 11(right), which displays the mean amplitude of the normal force coefficient, ĉN (see eq. 9), as a function of the reduced frequency. The trend is parabolic for all foils. It becomes obvious from this figure that flexibility can contribute to lower structural loads compared to the rigid reference, decreasing the cyclic stress, which translates into exponential increase in structural lifetime.

The thrust efficiency η is also displayed as a function of the reduced frequency in fig. 12. All curves show improved characteristics with increasing k o . For the same reasons as above, no maxima can be obtained. Nevertheless, the most flexible foil is clearly advantageous over the whole examined range, delivering an improvement ranging from 35 % (high k o ) to 75 % (low k o ).

Results for λ = 3

The motion law for λ=3 (eq.2) results in a maximum angle α max =20°. The setup for λ=3 begins at k o =0.033; the reduced frequency is then increased step-wise until it reaches k o =0.653. For all measurements carried out at λ=3, the measured drag for the first half of the period is partially negative. This unphysical behavior is a consequence of the sensor's cross-talk and hysteresis, combined with the low magnitude of the forces (see section 3 for details). Rigid hydrofoil: Lift increases together with angle of attack up to the static stall angle α stall = 15°, reaching a wide and smooth maximum. An abrupt peak is visible at α max on both the ascending and descending branches. From this point on, the lift reduces until the flow reattaches at the zerocrossing, where the lift is zero. Differences with the λ=2 case displayed in fig. 9, where the stall occurred far before α max , are a consequence of the different maximum angle, but may also be affected by the higher value of k o . The drag features a peak at the stall point, whose magnitude in the ascending branch is 55 % larger than in the descending branch.

Flexible hydrofoils: The lift curves are smoothed out compared to those of the rigid foil. The lift developed by the most flexible foil slightly overtakes that of the rigid foil. All foils develop zero lift at the zero crossing. Rigid hydrofoil: The lift reaches a larger maximum (c Lmax =1.6) at a higher angle (α=19°) than at the lower-frequency case.

The dynamic stall characteristics are less significant; however, hysteresis with negative lift at zero-crossing, and smoother characteristic lift and drag peaks at the stall point can be reported, particularly in the ascending branch.

Flexible hydrofoils: The lift curves are smoothed out for all flexible foils, except for the intermediate foil (t=0.5 mm) which features a stall peak shortly before α max . The most flexible foil (t=0.3 mm) provides slightly higher lift than the rigid foil, al- λ=3 it is probable that strut and tip losses, blade-blade interaction effects and friction would exceed the thrust for high reduced frequencies, which correspond to high turbine solidity.

Figure 16 (right) displays the value of ĉN for all four foils: no influence of flexibility on the lifetime is evidenced in the case λ=3.

Finally, the thrust-to-normal-force ratio η is shown in fig. 17. The rigid foil displays a steep trend, with magnitude similar to that of the most flexible foil at k o =0.35. For both lower and higher values of k o , the flexible foil provides better performance.

Conclusions

The effect of blade flexibility on the performance of VAWT has been investigated experimentally in this study, particularly in regimes featuring dynamic stall. The main results may be summarized as follows:

• At λ=2 a significant improvement in the delivered thrust is observed when using the most flexible foil. This is in accordance with McPhee and Beyene [START_REF] Macphee | Fluid-structure Interaction analysis of a morphing vertical axis wind turbine[END_REF] who studied a threebladed vertical-axis wind turbine numerically and reported a significant improvement of the rotor efficiency. The most flexible blade provided the highest improvement. This advantage reduces with increasing values of k o , so that the foil with intermediate flexibility becomes more advantageous for higher values of k o . Very significant improvements in both the thrust-to-normal-force ratio and stress reduction are observed when using the most flexible foil. These improvements are explained by the lift and drag measurements, which show that much lower levels of drag and significantly smoother drag variations are obtained near the stall region, while the reduction in lift is comparatively small.

• At high tip speed ratio (λ=3), a minor advantage is seen when using highly flexible foils, particularly so at high and low reduced frequencies. Nevertheless, the low magnitude of the hydrodynamic forces results in relatively high experimental uncertainty for λ=3, so that these observations must be taken with caution. The benefits of the bending mechanism for the flexible foil are also less significant as the maximum angle of incidence diminishes with raising λ.

These results support following conclu-sions:

1. The surrogate model used in this and in previous studies permits the de 2. Blade flexibility delivers promising improvements to the operational characteristics of VAWT. At commonly employed tip speed ratios, where dynamic stall and strong hysteresis become dominant flow phenomena, blades with high flexibility deliver significantly higher torque. This is due to their favorable behavior near the stall region, where they feature lower drag at comparable levels of lift.

3. The flexibility in VAWT blades translates into large increases in thrust efficiency (thrust-to-normal-force ratio), reducing the inner structural loads associated with normal forces. They also feature significantly reduced stress amplitude (average amplitude concerning cyclic variations of normal force), which translates into reduced fatigue-related lifetime limitations if the profile design is adapted to provide enough contributing cross-section area to distribute the force over the structure.

Further work should include a broader range of operation, with a quantitative translation of blade performance parameters into the turbine reference frame. This would allow the exploration of a wider range of turbine designs, and the identification of optimal blade stiffness (present data suggests that this is a function of reduced frequency). Furthermore, using particle image velocimetry measurements as well as surface-tracking methods would deepen our understanding of the fluid and structural dynamics of the deforming blades.

αF

  max maximum angle of incidence [rad] α stall angle of incidence with onset of stall [rad] α angular velocity of the pitching foil dα dt [rad/s] η thrust-to-normal force ratio [-]λ tip speed ratio, λ = ω D R v∞ [-] ρ density [kg/m 3 ] σ solidity σ = n•C R [-] channel inlet velocity [m/s] I second moment of inertia [m 4 ] xyz forces in xyz dimensions [N] T xyz torque in xyz dimensions [N m]N number of cycles before material failure[-]

Figure 1 :

 1 Figure 1: Left and middle: velocity triangles and hydraulic forces on a VAWT at λ ≈ 2.2 for four azimuth angles: the angle of incidence varies with azimuth angle θ and tip-speed ratio. Only the tangential part (sinusoidal share) of the lift force generates thrust. Most of the hydrodynamic forces result in structural loads. Drag forces were scaled up for better readability. Right: CAD model of a three-bladed H-Darrieus turbine rotor.

Figure 2 :

 2 Figure 2: Left: The compound hydrofoil consists of a leading edge milled from aluminum, a skeleton of carbon and a body of silicone. The rigidity of the foil is adjustable through the thickness of the carbon core. It is mounted on a six-axes load cell via an aluminum base plate. Right: The most flexible design (carbon blade thickness 0.3 mm) performs large deformations during one period. The picture shows the deflection for the λ=3 case at α = 20 °ready

Figure 3 :

 3 Figure 3: Normalized angle of incidence α and pitch speed α for λ=2. The non-harmonic trajectory leads to a maximum absolute pitch speed in the descending branch. This has to be considered in the definition of k D and k o .

Figure 4 :

 4 Figure 4: Reference frame of the measurement with qualitative forces and coefficients. Thrust and normal loads are the sinusoidal and cosine shares of lift and drag. v ch becomes equivalent to the relative velocity w. The measured forces and moments F xyz , M xyz from the rotating sensor get transformed to the channel coordinate system and become F xyz and M xyz (see sec.3)

Figure 5 :

 5 Figure 5: Influence of λ and k D on turbine design, and region investigated in this study. Thin structures with high λ are characterized by low k D , while massive structures with low λ lead to high k D . The value of k D diminishes with increasing λ as the maximum angle reduces; while k D increases with raising solidity as the relation of the chord length C to the turbine radius R grows. For visualization purposes, solidity σ is calculated here for a three-bladed turbine, k D and k o include C/R (see eqs.(10)&(12)).

Figure 6 :

 6 Figure 6: Experimentally-measured deflection of the flexible foil (for t=0.3mm) at λ=2 and angle of incidence α = 30°. The acquisition was made with a Phantom V2511 high-speed camera, colors were inverted, and the non-deformed shape for the same position was later added to the plot. The deformation changes the shape of the foil; in consequence it behaves like a high-cambered foil operating at lower angle of incidence.

Figure 7 :

 7 Figure 7: Experimental setup: Left: Detail of shaft, sensor and foil; right: test section at LEGI Grenoble with a streamwise length (X-axis) of 1000 mm, a spanwise width (Z-axis) of 175 mm and a height (Y -axis) of 280 mm. The closed water channel can run up to 600 l s -1 volume flow rate. The foil rotation center, at 1/4 chord length, is placed 300 mm downstream of the inlet.

Figure 8 :

 8 Figure 8: Comparison of the experimental measured drag (top) and lift (bottom) coefficients with calculated values. The grey fields are the min/max variations from mean value. The results show satisfactory agreement with Javafoil and with the theoretical slope (c L = 2π sin(α)) below the static stall angle of ≈15°.

4. 1 2 4. 1 . 1

 1211 Results for λ = Transitional state at k o = 0.026 (fig. 9 (left)):Rigid hydrofoil: From starting point θ = 0 the lift increases with the angle of incidence until the static stall angle of α=15°( c L =1.4). The lift remains constant until it suddenly decreases to c L =0.8 at α=19°after a short peak to c L =1.7. It then remains almost constant with further losses after α max is reached; a small positive peak is visible when the flow reattaches at α=7.5°. At the zero-crossing (when the profile becomes horizontal), c L is zero. The drag coefficient c D is very low for α < α stall and remains in the range of the measurement uncertainty. When the stall point is reached, c D displays a large peak and then remains at a high value, increasing until α max is reached. The drag then steeply decreases until the flow reattaches: There again c D becomes lower than the measurement uncertainty.Flexible hydrofoils: The flexible foils provide a smoother trend than the rigid foil. None of the three foils feature a pointed peak, on either the lift or the drag curves. Apart from the area close to the stall point, all flexible foils display values of c L similar in magnitude to those of the rigid foil, while their values for c D are significantly reduced in the stalled regime.

4. 1 . 2

 12 Dynamic stall at k o = 0.277 (fig. 9 (right)):

Figure 9 :

 9 Figure 9: Results at λ=2 for four NACA0018 hydrofoils: one rigid and three flexible foils with different blade thicknesses: [0.3, 0.5, 0.7] mm. The black sinusoidal curve in the upper plots displays the angle of attack α [ • /10• ], with α max =30°. Left: Transitional state at k o =0.026; Right: Full dynamic state with deep dynamic stall at k o =0.277;

4. 1 . 3

 13 Dynamic stall at k o = 0.46 (fig. 10 (left)):

Figure 10 :

 10 Figure 10: Results at λ=2 for four NACA0018 hydrofoils: one rigid and three flexible foils with different blade thicknesses: [0.3, 0.5, 0.7] mm. The black sinusoidal curve in the upper plots displays the angle of attack α [ • /10 • ], with α max =30°. Left: Fully-dynamic state at k o =0.46; Right: Fully-dynamic state at k o =0.71.

Figure 11 :

 11 Figure 11: Left: Thrust coefficient c T , a measure for the qualitative performance, as a function of reduced frequency. Right: Amplitude of the normal coefficient (ĉ N ), an indicator for the turbine lifetime, as a function of the reduced frequency k o . Lower values are favorable, since lifetime rises exponentially with diminishing stress; A second-order polynomial curve fit of the data was added. These results correspond to λ=2 for four NACA0018 hydrofoils: one rigid and three flexible foils with different blade thicknesses: [0.3, 0.5, 0.7] mm.

Figure 12 :

 12 Figure 12: Thrust-to-normal-force ratio η, a measure for the benefit-to-cost ratio, as a function of reduced frequency. λ=2 for four NACA0018 hydrofoils: one rigid and three flexible foils with different blade thicknesses: [0.3, 0.5, 0.7] mm.

4. 2 . 1

 21 Transitional/dynamic state with dynamic stall at ko=0.069 (fig. 13 (left)):

4. 2 . 2

 22 Dynamic state at k o =0.130 (fig. 13 (right)):

Figure 13 :

 13 Figure 13: Results at λ=3 for four NACA0018 hydrofoils: one rigid and three flexible foils with different blade thicknesses: [0.3, 0.5, 0.7] mm. The black sinusoidal curve in the upper plots displays the angle of attack α [ • /10 • ], with α max =20°. Left: Transitional state at k o =0.069; Right: state at k o =0.130;

Figure 14 :

 14 Figure 14: Results at λ=3 for four NACA0018 hydrofoils: one rigid and three flexible foils with different blade thicknesses: [0.3, 0.5, 0.7] mm. The black sinusoidal curve in the upper plots displays the angle of attack α [ • /10 • ], with α max =20°. Left: Fully-dynamic state at k o =0.241; Right: Fully-dynamic state at k o =0.344;

Figure 15 :Figure 16 :

 1516 Figure 15: Results at λ=3 for four NACA0018 hydrofoils: one rigid and three flexible foils with different blade thicknesses: [0.3, 0.5, 0.7] mm. The black sinusoidal curve in the upper plots displays the angle of attack α [ • /10 • ], with α max =20°. Left: Fully-dynamic state at k o =0.486; Right: Fully-dynamic state at k o =0.653;

Figure 17 :

 17 Figure 17: Thrust-to-normal-force ratio η, a measure for the benefit-to-cost ratio, as a function of reduced frequency. Results at λ=3 for four NACA0018 hydrofoils: one rigid and three flexible foils with different blade thicknesses: [0.3, 0.5, 0.7] mm.

  tailed study of parameters such as blade flexibility over a very wide range of design points, reproducing the flow regimes corresponding to multiple tip speed ratios and turbine solidities through the choice of the reduced frequency and the oscillation trajectory. It allows relating improvements in performance indicators (c T , η, ĉN ) to the fluid dynamic properties found in the reference frame of the blade (c L and c D curves). In the present case, the benefit of using a flexible structure for a given operating point may be assessed simply by reporting c T values from figs. 11(left and right) into the design parameter map in fig.5. However, the comparison between multiple design or operating points (k o and λ) requires a transformation of the results in the turbine reference frame, which would include different rotational speeds as a function of λ and R, and of torque as a function of c T and R, which depend on the design point. Then, sec-ondary effects (upstream wake in the downstream part of the rotor, bladeblade interaction) would play a significant role.

Table 1 :

 1 Parameters of the experiment Symbol unit value

	Tip-speed ratio	λ	-	[2.0, 3.0]
	Composite plate thickness	t	m	[0.3, 0.5,0.7]
	reduced frequencies (λ=2)	k o	-	[0.03, 0.06, 0.16,
				0.28, 0.33, 0.46, 0.71]
	reduced frequencies (λ=3)	k o	-	[0.03, 0.07, 0.13, 0.24,
				0.34, 0.49, 0.62, 0.65]
	quency of 6.45 Hz. In both cases, an upper
	limit was set on f o in order to prevent reso-
	nance damage on the load cell. The oscilla-
	tion was performed over 10 s for each step.
	Figures 9-10 display the lift and drag coef-
	ficients over one normalized oscillation pe-
	riod T for λ=2, and figs.13-15 display those
	same values for λ=3. The upper plot (lift co-
	efficients over one period) also includes the
	trajectory of the angle of incidence, which is
	plotted unitless ([

• /10 • ]) to fit with the lift coefficients. The plot maps the mean values for all normalized periods within the measurement time of 10 s, with the first and last periods excluded. Only a selection of the investigated frequencies is shown, including minimum, intermediary and maximum values for k o . Variations of the inlet velocity v ch lead to differences in k o for constant f o . This means that k o is the mean frequency for each frequency step.

Acknowledgements

The corresponding author is grateful for the funding of his thesis by the Rosa-Luxemburg-Stiftung Berlin, the Wachstumskern Flussstrom Plus project, financed by the German Federal Ministry of Education and Research, and the funding of German-French-University Saarbrücken.

The authors thank the Unité Mixte de Service Grenoble-Alpes Recherche Infrastructure et Calcul Intensif et de Données (UMS-GRICAD) for their services. The support of Michael Haarman (CATLAB, Berlin), Michel Riondet and Jean-Marc Barnoud (LEGI, Grenoble) is gratefully acknowledged.


Ingrid Marie Andersen
email: mia.andersen@cemes.fr

Luis Alfredo

Rodríguez González

Cristina Bran

Cécile Marcelot

Sébastien Joulié

Teresa Hungría

Manuel Vazquez

Christophe Gatel
email: christophe.gatel@cemes.fr.

Etienne Snoeck

Sébastien

Luis Alfredo Rodríguez

Sébastien Joulie

Teresa Hungria

Exotic Transverse-Vortex Magnetic Configurations in CoNi Nanowires

Keywords: magnetic configuration, magnetic nanowire, electron holography, vortex state, micromagnetic simulation, nanocylinder

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

One-dimensional magnetic nanostructures have for the past two decades been of increased interest for the development of future spintronic devices [START_REF] Bocklage | Dependence of Magnetic Domain-Wall Motion on a Fast Changing Current[END_REF][START_REF] Rodríguez | Optimized Cobalt Nanowires for Domain Wall Manipulation Imaged by In Situ Lorentz Microscopy[END_REF][START_REF] Ivanov | Modulated Magnetic Nanowires for Controlling Domain Wall Motion: Toward 3D Magnetic Memories[END_REF][START_REF] Da Col | Observation of Bloch-Point Domain Walls in Cylindrical Magnetic Nanowires[END_REF] motivated by concepts like Magnetic Race Track Memory [START_REF] Parkin | Magnetic Domain-Wall Racetrack Memory[END_REF] and the wish to manipulate magnetic domain walls (DW). Cylindrical nanowires (NWs) are particularly interesting candidates to reach this goal, much due to the fast DW motion induced by an external magnetic field or electric current, where theoretical studies have anticipated the absence of a Walker breakdown. [START_REF] Yan | Beating the Walker Limit with Massless Domain Walls in Cylindrical Nanowires[END_REF][START_REF] Hertel | Ultrafast Domain Wall Dynamics in Magnetic Nanotubes and Nanowires[END_REF] In addition, curvature effects have recently been proved to induce effects related to topology, chirality, and symmetry, [START_REF] Sander | Magnetism Roadmap[END_REF] and unidirectional reversal process has been reported by engineering the geometry in multi-segmented nanowires. [START_REF] Bran | Magnetization Ratchet in Cylindrical Nanowires[END_REF] However, to further technical developments in spintronics and a better control of DW motion, a thorough understanding of the fine structures of DWs in magnetic NWs, in which shape and crystal structure are contributing factors to the minimization of the system's magnetic energy, [START_REF] Ivanov | Crystallographically Driven Magnetic Behaviour of Arrays of Monocrystalline Co Nanowires[END_REF][START_REF] Biziere | Imaging the Fine Structure of a Magnetic Domain Wall in a Ni Nanocylinder[END_REF][START_REF] Gatel | Size-Specific Spin Configurations in Single Iron Nanomagnet: From Flower to Exotic Vortices[END_REF][START_REF] Ivanov | Magnetic Structure of a Single-Crystal Hcp Electrodeposited Cobalt Nanowire[END_REF] is required.

The magnetic configurations in various Co-based cylindrical nanowires have previously been studied in several publications, [START_REF] Ivanov | Magnetic Structure of a Single-Crystal Hcp Electrodeposited Cobalt Nanowire[END_REF][START_REF] Berganza Eguiarte | Multisegmented Nanowires: A Step towards the Control of the Domain Wall Configuration[END_REF][START_REF] Piao | Intrinsic Pinning Behavior and Propagation Onset of Three-Dimensional Bloch-Point Domain Wall in a Cylindrical Ferromagnetic Nanowire[END_REF][START_REF] Maaz | Effect of Crystallographic Texture on Magnetic Characteristics of Cobalt Nanowires[END_REF] which have revealed a strong influence of the NW's structural properties, [START_REF] Reyes | Magnetic Configurations in Co/Cu Multilayered Nanowires: Evidence of Structural and Magnetic Interplay[END_REF] and thus a dependence of their fabrication process. [START_REF] Ivanov | Crystallographically Driven Magnetic Behaviour of Arrays of Monocrystalline Co Nanowires[END_REF][START_REF] Vega | Tuning the Magnetic Anisotropy of Co-Ni Nanowires: Comparison between Single Nanowires and Nanowire Arrays in Hard-Anodic Aluminum Oxide Membranes[END_REF][START_REF] Cho | Control of Magnetic Anisotropy of Co Nanowires[END_REF] For instance, it has been shown that monocrystalline hcp phase can be obtained in pure Co NWs with the c-axis engineered with nearly perpendicular orientation to the NW axis. [START_REF] Ivanov | Crystallographically Driven Magnetic Behaviour of Arrays of Monocrystalline Co Nanowires[END_REF][START_REF] Liu | Shape Anisotropy and Magnetization Modulation in Hexagonal Cobalt Nanowires[END_REF] The corresponding uniaxial magnetocrystalline anisotropy is then strong enough to challenge the large shape anisotropy of NWs. [START_REF] Ivanov | Crystallographically Driven Magnetic Behaviour of Arrays of Monocrystalline Co Nanowires[END_REF][START_REF] Garcı Á | Magnetic Behavior of an Array of Cobalt Nanowires[END_REF][START_REF] Ferré | Magnetization Processes in Nickel and Cobalt Electrodeposited Nanowires[END_REF] In CoNi-alloy NWs, the amount of Ni content can modify the crystallographic phase: while Co NWs with a low Ni content keep a hcp phase with a strong magnetic anisotropy and a resulting magnetic induction perpendicular to the NW axis, high Ni content generally leads to fcc crystal structure with a lower magnetocrystalline anisotropy [START_REF] Barriga-Castro | Pseudo-Monocrystalline Properties of Cylindrical Nanowires Confinedly Grown by Electrodeposition in Nanoporous Alumina Templates[END_REF][START_REF] Carl | HCP-FCC Phase Transition in Co-Ni Alloys Studied With Magneto-Optical Kerr Spectroscopy[END_REF] and a parallel magnetic induction. Tuning the CoxNi1-x content then allows for adjusting the magnetic easy axis orientation from parallel (with cubic anisotropy) to perpendicular (with uniaxial anisotropy) relative to the nanowire axis, [START_REF] Ivanov | Crystallographically Driven Magnetic Behaviour of Arrays of Monocrystalline Co Nanowires[END_REF][START_REF] Samardak | Variation of Magnetic Anisotropy and Temperature-Dependent FORC Probing of Compositionally Tuned Co-Ni Alloy Nanowires[END_REF] making CoNi-alloy NWs interesting as potential building blocks for future devices.

However, previous publications have shown a coexistence of fcc and hcp crystal phases in single CoNi alloy NWs, [START_REF] Barriga-Castro | Pseudo-Monocrystalline Properties of Cylindrical Nanowires Confinedly Grown by Electrodeposition in Nanoporous Alumina Templates[END_REF][START_REF] Samardak | Variation of Magnetic Anisotropy and Temperature-Dependent FORC Probing of Compositionally Tuned Co-Ni Alloy Nanowires[END_REF] but there has been little or no report on how they mix and affect the magnetic configuration of the NW.

Only statistical overviews of the structural and chemical information have been reported, as the crystal phase and composition in NWs are often determined by techniques like x-ray diffraction (XRD) and energy dispersive x-ray microanalysis (EDX) on assemblies or arrays of NWs. [START_REF] Ivanov | Crystallographically Driven Magnetic Behaviour of Arrays of Monocrystalline Co Nanowires[END_REF][START_REF] Vega | Tuning the Magnetic Anisotropy of Co-Ni Nanowires: Comparison between Single Nanowires and Nanowire Arrays in Hard-Anodic Aluminum Oxide Membranes[END_REF] To gain control over the magnetization states and reversal mechanisms, a precise analysis of the local structure of a single nanowire, combined with its magnetic configuration, is required. A quantitative study of both the structure and the magnetic properties obtained on the same area, and at the nano-scale, demands versatile and advanced techniques in combination with sufficient spatial resolution and sensitivity. Off-axis electron holography (EH) carried out in a transmission electron microscope (TEM) is an appropriate interferometric technique that allows for imaging of the magnetic configuration in nanostructures with nanometer resolution and high sensitivity. [START_REF] Mccartney | Electron Holography: Phase Imaging with Nanometer Resolution[END_REF][START_REF] Staňo | Probing Domain Walls in Cylindrical Magnetic Nanowires with Electron Holography[END_REF][START_REF] Snoeck | Quantitative Magnetization Measurements on Nanometer Ferromagnetic Cobalt Wires Using Electron Holography[END_REF][START_REF] Gandha | High Energy Product Developed from Cobalt Nanowires[END_REF][START_REF] Cantu-Valle | Mapping the Magnetic and Crystal Structure in Cobalt Nanowires[END_REF] EH offers quantitative information on the in-plane components of the magnetic induction inside the sample, as well as of the stray field surrounding it (see supplementary information S2). As EH is based in a TEM environment, it offers the advantage of combining other TEM techniques, like high-resolution TEM (HRTEM), selected area electron diffraction (SAED) and electron energy loss spectroscopy (EELS), and thus allows for studying the crystal structure and composition of the same area of the same NW with a high spatial resolution. In this work, we have combined EH with conventional TEM, Scanning TEM (STEM)-EELS and ASTAR measurements, a diffraction spot recognition technique based in the TEM (see supplementary information S3), to image and quantitatively determine the magnetic induction of small diameter cylindrical NWs of nominal composition Co85Ni15, i.e. NWs with a low Ni content, prepared by electrodeposition (see supplementary information S1), in relation to their local crystallographic structure and chemical composition. In addition, micromagnetic OOMMF simulations have been carried out for a deeper analysis of the local magnetic microstructure. This correlative study of TEM methods combined with micromagnetic simulations, allowed us to determine the key factors that govern the main parameters involved the magnetic configuration.

For the sake of consistency, all the results presented in this work are taken from the same area of a single nanowire, representative for the whole sample. Similar results were obtained from other NWs of the same batch. The length of the enclosed area is 1.7 µm. EH analysis was carried out in this area and is shown in Figure 1c and1d. Figure 1c displays the magnetic phase shift obtained at remanent state with a spatial resolution of 3 nm, and Figure 1d highlights the magnetic flux by applying a cosine function on the amplified version of the magnetic phase image in Figure 1c. A first analysis indicates that this NW displays a very complex magnetic configuration with four different magnetic regions, marked C1 to C4. The magnetic configuration in regions C1 and C4 in Figure 1c, presents isophase lines oriented parallel to the nanowire axis (x-axis as indicated by white arrows), evidencing an in-plane magnetic flux running along the NW axis and therefore a net component of the magnetization parallel to the NW axis. In contrast, the second prominent configuration of magnetic isophase lines, marked C2 in Figure 1c, displays a chain of circular patterns, aligned periodically in the middle of the nanowire. These curling isophase lines separate regions with magnetic flux pointing in opposite directions (marked by white arrows). This magnetic pattern corresponds to an antiparallel domain-like region whose magnetization is oriented perpendicular to the nanowire axis (marked by arrows along y-axis) with alternating opposite direction. Such a configuration is expected in NWs with magnetization easy axis oriented perpendicular to the nanowire axis as a consequence of a perpendicular magnetocrystalline anisotropy strong enough to counterbalance the NW shape anisotropy, which tends to align the magnetization parallel to its axis. The antiparallel coupling between adjacent domains allows for minimizing the dipolar energy. Lastly, the region marked C3 in Figure 1c bears resemblance to region C2, but with the isophase lines slightly oriented towards the nanowire axis, when compared to the C2 region. C3 region thus seems to be an intermediate state between C4/C1 and C2 regions. Our results thus demonstrate that three distinctly different magnetic domains appear within a limited length of the NW. We start a deeper analysis of the magnetic phase image by focusing our attention on the C1 and C4 areas, presenting a net component of the magnetization parallel to the NW axis. By measuring the magnetic phase shift across the NW in each of the C1-4 regions (marked in Figure 1c by red and grey arrows, and plotted in Figure 1e) and assuming a circular NW cross section with a uniform magnetization along the x-axis, we can extract the value of the in-plane magnetic induction parallel to the NW axis in the selected regions (see supplementary information S2). Using equation 6 from S2, we measure a magnetic induction of 0.7 T in C1 and 1 T in C4, while the expected saturation magnetization in Co85Ni15 alloy NWs, with all magnetic moments aligned parallel to the NW axis, is 1.6 T. [START_REF] Bran | Direct Observation of Transverse and Vortex Metastable Magnetic Domains in Cylindrical Nanowires[END_REF] It then comes out of our experimental measurements that either the composition of the Co85Ni15 alloy is far from the one expected, leading to a strong decrease of the magnetization, or there is no region with a uniform magnetization parallel along the NW, even though the isophase lines in regions C1 and C4 indicate at it to be at least partly aligned along the axis. However, the hypothesis concerning a large deviation of the alloy composition is not valid: such magnetization values would correspond to a high Ni content of more than 70%. This is in contradiction with our TEM spectroscopy measurements as well as previous studies performed on similar NWs elaborated by the same procedure, [START_REF] Bran | Direct Observation of Transverse and Vortex Metastable Magnetic Domains in Cylindrical Nanowires[END_REF] where a mean value of 15% Ni is expected. We thus conclude that the magnetization is not uniform and present a rotating component around the NW. In addition, the difference between measured values in regions C1 and C4 clearly indicates that even if the magnetic configuration looks similar in these regions, their total magnetic induction components parallel to the NW axis are different, and lower in the former compared to the latter. This is qualitatively evidenced in Figure 1d, where the magnetic flux line density is much higher in the C4 region compared to C1. Like all other TEM methods, EH is a projection technique: the phase shift of the electron beam related to the inplane magnetic induction components, is integrated along the beam path. In addition, EH is only sensitive to the components of the magnetic induction perpendicular to the beam path, i.e. in-plane magnetic components (see Supplementary Information S2 for details). In case of a rotation of the magnetization around the NW axis, no integrated in-plane magnetic induction would be detected by EH as each magnetic induction component would have an equal, but opposite counterpart or will contain an out-of-plane component. As a result, the integration along the beam line would give zero phase shift, and only the remaining component along the NW axis would contribute to the phase shift. Accordingly, the magnetic configuration and the low phase shift value measured by EH in regions C1 and C4, indicate that a part of the magnetic induction presents a rotation around the NW axis. Two magnetic configurations, combining both rotating and parallel magnetic components, could in principle be considered: either a vortex state or a partial magnetic curling state around the NW axis. The possibility of vortex state is disregarded as it should give rise to inhomogeneous magnetization. The magnetic curling state has been reported by Ruiz-Gómez et al. [START_REF] Ruiz-Gómez | Observation of a Topologically Protected State in a Magnetic Domain Wall Stabilized by a Ferromagnetic Chemical Barrier[END_REF] and is described by a magnetization at the core of the NW pointing in the direction of the nanowire axis, surrounded by a helical magnetic configuration. As previously stated, we observe a change in measured induction between regions C1 and C4 (Figure 1e) that could arise from a difference in size of the core of such a vortex state as discussed by Bran et al. and Ivanov et al. [START_REF] Bran | Direct Observation of Transverse and Vortex Metastable Magnetic Domains in Cylindrical Nanowires[END_REF][START_REF] Ivanov | Single Crystalline Cylindrical Nanowires -Toward Dense 3D Arrays of Magnetic Vortices[END_REF] or from a change in rotation angle of the curling with respect to the nanowire axis. The distribution of the magnetic shift and deeper analysis suggest that it is the curling state that occur in our system, where the highest phase shift value in region C4 comes from a smaller curling angle, i.e. a more elongated rotation along the nanowire axis, and thus a stronger measured magnetic induction.

RESULTS AND DISCUSSION

Moving on, region C2 in Figure 1c bears evidence of antiparallel magnetic domain-like regions oriented perpendicular to the nanowire axis (along the y-axis), separated by states depicting a circular shape. These antiparallel domain-like regions are separated by a series of vortex states where the magnetization direction of the vortex core is oriented perpendicular to the nanowire axis (along the z-axis) with alternating chirality (rotation of the in-plane magnetization) or polarity (magnetic core orientation). Note the surprising exotic magnetic configuration where the transverse domain-like regions are significantly smaller in size than the vortex states. Finally, the C3 segment in Figure 1c looks like a transition region between the two already presented magnetic configurations (perpendicular vortex chain, and curling state) in C2 and C4: from C2 the vortex states disappear and the magnetic flux parallel to the NW axis increases as we move towards C4. To understand why this nanowire presents this complex magnetic configuration, we performed structural and chemical analysis on the same nanowire area, as shown in Figure 2a-e. ASTAR measurements were carried out to determine the local crystalline structure within the NW by retrieving precession diffraction patterns of the nanowire region (Figure 2a show mapped area), which were then analyzed by comparison to a database of calculated diffraction patterns using the automatic pattern recognition software of ASTAR NanoMEGAS [START_REF] Viladot | Orientation and Phase Mapping in the Transmission Electron Microscope Using Precession-Assisted Diffraction Spot Recognition: State-of-the-Art Results[END_REF][START_REF] Rauch | Automated Nanocrystal Orientation and Phase Mapping in the Transmission Electron Microscope on the Basis of Precession Electron Diffraction[END_REF] (See supplementary information S3 for more details). The results, as seen in Figure 2b-e, show that the region generally consist of three crystal grains: two fcc and one hcp crystal phase grains were found to coexist in the nanowire segment. The appearance of two phases has already been documented in CoNi alloyed NWs in literature. [START_REF] Barriga-Castro | Pseudo-Monocrystalline Properties of Cylindrical Nanowires Confinedly Grown by Electrodeposition in Nanoporous Alumina Templates[END_REF][START_REF] Samardak | Variation of Magnetic Anisotropy and Temperature-Dependent FORC Probing of Compositionally Tuned Co-Ni Alloy Nanowires[END_REF][START_REF] Bran | Direct Observation of Transverse and Vortex Metastable Magnetic Domains in Cylindrical Nanowires[END_REF] Contrary to previous results where different phases were observed in different regions of the NW, we here see that the grain boundaries between the fcc and hcp phases are running almost parallel to the NW axis (Figure 2e). Thus, the two phases are coexisting within the same cross-section in regions of the NW but not with the same proportion along the NW. ASTAR experiments (Figure 2c) also indicate that the grains' close-packed directions [111]fcc and [0001]hcp are close to perfectly aligned with respect to the y-axis (perpendicular to the nanowire axis), making a transition from one crystal phase to the other possible by stacking fault. Figure 2c-d also show that the c-axis of the hcp structure is on average oriented 78 relative to the nanowire axis, i.e. almost perpendicular to it.

By overlapping the magnetic phase shift image onto the same region of the crystal phase map extracted from ASTAR (Figure 2f), we observe that the chain of vortex states (regions C2) is located on the area which consist mainly of hcp phase, indicating a direct correlation between the perpendicular magnetic configuration and the hcp structure with the [0001] direction (c-axis) at 78 relative to the NW axis (Figure 2c). It is well known that fcc and hcp crystal phases have different types magnetocrystalline anisotropy (uniaxial for hcp phase, and cubic for fcc phase), with different values of the anisotropy constant, [START_REF] Carl | HCP-FCC Phase Transition in Co-Ni Alloys Studied With Magneto-Optical Kerr Spectroscopy[END_REF][START_REF] Scarani | The Microstructure of Electrodeposited Cobalt-Based Nanowires and Its Effect on Their Magnetic and Transport Properties[END_REF] and consequently different easy axis directions. The local change of crystal phase is therefore assumed to be the origin of changes in magnetic configuration, and it is likely the magnetocrystalline anisotropy of the hcp phase that favors the magnetization alignment along the c-axis, as it is strong enough to challenge the shape anisotropy of the NW, which in turn promotes a stronger transverse magnetic component. [START_REF] Henry | Magnetic Anisotropy and Domain Patterns in Electrodeposited Cobalt Nanowires[END_REF] To gain a deeper understanding of the complex magnetic configuration observed by EH, we performed a static micromagnetic simulation of the remnant state by the use of OOMMF code. [START_REF] Donahue | OOMMF User's Guide[END_REF] We used the magnetic parameters for a Co85Ni15 monocrystalline hcp phase structure for the hcp grain, [START_REF] Bran | Direct Observation of Transverse and Vortex Metastable Magnetic Domains in Cylindrical Nanowires[END_REF] with saturation magnetization Ms = 1273 kAm - 1 , 31 a value of the exchange constant A = 26 x 10 -12 Jm -1 , and using an uniaxial magnetocrystalline anisotropy value of K1 = 350 kJm -3 oriented at 78 relative to the NW axis, as found by ASTAR for the hcp grain in the NW sample. Figure 3 shows the main results of the micromagnetic simulations, where Figure 3a shows the three-dimensional simulated magnetization at remanent state obtained from OOMMF calculations, where the x-y-plane of the magnetic vectors are represented by the colored directions of the color wheel. Figure 3b shows the simulated magnetic phase image calculated from the micromagnetic simulations, and the corresponding flux image is shown in Figure 3c We obtain a nice agreement between the experimental (region C2 in Figure 1c) and the simulated phase image (Figure 3b), allowing for a determination of the involved magnetic parameters through the OOMMF simulation. Local chemical analyses were performed by spectrum images in Scanning Transmission Electron Microscopy -Energy Electron Loss Spectroscopy (STEM-EELS) mode to elucidate the origin of the observed hcp/fcc structure change. We focused our STEM-EELS analysis around the hcp-fcc grain boundary, which is visible in the bright field TEM image in Figure 4a and corresponds to the magnetic configuration shown in Figure 4b. From spectrum imaging experiment carried out on the L2,3 edge of Co and Ni, we have extracted Co and Ni content maps (Figure 4c and4d) using multiple linear least squares (MLLS) fitting. [START_REF] Longo | Atomic Elemental and Chemical Analysis of SrTiO3/LaMnO3 Multilayers Using Fast Simultaneous EELS and EDS Analysis in Digi-talMicrograph[END_REF] These maps reveal a difference in composition between the two grains; the region of hcp structure show a higher Co concentration (average of 89% Co and 11% Ni in square I in Figure 4c) as compared with the fcc structure (average of 80% Co and 20% Ni in square II in Figure 4d), which appears contain less Co. This agrees well with Co-Ni phase diagrams, where hcp phase appears in Co-rich [Co-Ni] alloys. [START_REF] Carl | HCP-FCC Phase Transition in Co-Ni Alloys Studied With Magneto-Optical Kerr Spectroscopy[END_REF] The lowest Co content in square I is 85.5%, while the highest Co content in square II is 82%. This point to a compositional threshold around 80-85% of Co to stabilize hcp phase, which is higher than the previously reported threshold of 70-75% Co [START_REF] Carl | HCP-FCC Phase Transition in Co-Ni Alloys Studied With Magneto-Optical Kerr Spectroscopy[END_REF][START_REF] Nishizawa | The Co-Ni (Cobalt-Nickel) System[END_REF] at room temperature for film or in the bulk. However, a more systematic and extensive study of this must be made to clearly conclude an accurate threshold, which partly depends on the elaboration process.

The chain of vortex states is located in the large grain of mainly hcp phase (C2), and the curling state seems to be located in regions with a coexistence of fcc and hcp phase grain (C1 and C4). Spectrum imaging and ASTAR experiments indicate that the magnetic transition region C3 is located almost along the hcp/fcc grain boundary, where both the structure and the composition is likely to change. The drastic changes in magnetic configuration appear to be caused by local changes in crystal structure induced by inhomogeneous composition of the NW. Even for small-to-moderate changes in composition (Detected Ni content of 8-25%, excluding edge measurements), results in a change in the crystal structure, and from this, a drastic difference in the local magnetic configuration.

CONCLUSIONS

Quantitative and local studies of the magnetic, structural and chemical changes have been performed on cylindrical textured Co-rich CoNi nanowires. A complex and inhomogeneous magnetic configuration has been revealed, consisting of a periodical configuration of exotic antiparallel transverse domain-like regions separated by transversvortex states of alternating chirality and/or polarity at the hcp rich region. In turn, in the more fcc rich regions, mostly axial domains are observed. A transition between these two regions has also been identified. The experimental results have been compared to micromagnetic simulations, revealing that the vortex chain is formed inside hcp phase of the Co-rich CoNi alloy. Correlated local changes in composition and crystal structure have been highlighted as the origin of the different magnetic configurations: the vortex chain is a result of the hcp phase whose magnetic easy axis (c-axis) is oriented 78 relative to the NW axis (x-axis), and counterbalances the shape anisotropy. A curling state with a magnetic induction component oriented along the NW axis is appearing in regions with fcc phase grains where the easy axis and shape anisotropy act in the same way. A transition region between these two configurations is observed at the fcc/hcp grain boundary running almost parallel to the NW axis.

This study demonstrates the strong correlations between crystal structure and composition, and consequently on the magnetic configurations in CoNi NWs. The effect of local crystalline changes due to a slight variation of composition is found to drastically change the magnetic configuration in the NW, and can therefore not be neglected when attempting to explain and analyze the magnetic structure. A correlative microscopy investigation has been a great advantage in this work, as it offers magnetic, structural and spectroscopic analysis of the exact same area, since the same sample can be inspected by the different microscopic techniques.

METHODS

Cylindrical CoNi nanowires were prepared by electrodeposition into self-assembles pores of anodic aluminum oxide templates. For a detailed description of the synthesis, see supplementary information S1. The NWs were drop casted onto a TEM carbon grid for the EH, STEM-EELS and ASTAR measurements.

Studies of the magnetic configuration of the CoNi NWs were performed by EH using a Hitachi HF-3300 (I2TEM-Toulouse) transmission electron microscope operated at 300kV. This microscope is equipped with a cold field emission gun, a spherical aberration corrector, and a double biprism setup, which makes it a dedicated microscope for interferometry experiments. The experiments were carried out in the normal stage of the I2TEM, at remanence state (with objective lens switched off), after an application of 1.8 T perpendicular to the sample, by switching the objective lens on and off again. The holograms were acquired by the use of a software for fringe position correction developed by C. Gatel, [START_REF] Gatel | Unlimited Acquisition Time in Electron Holography by Automated Feedback Control of Transmission Electron Microscope[END_REF] with an exposure time of 160 seconds per hologram, an inter-fringe distance of 1.5 nm, allowing for a spatial resolution of 3 nm for the treated magnetic phase images. For a more detailed description of the electron holography technique, see supplementary information S2.

Studies of the structural configuration of the NWs were performed on a Philips CM20-FEG TEM at 200kV using the NanoMEGAS ASTAR system, a TEM based automatic crystal orientation and phase mapping technique. [START_REF] Rauch | Automated Nanocrystal Orientation and Phase Mapping in the Transmission Electron Microscope on the Basis of Precession Electron Diffraction[END_REF] The data was acquired using precession electron diffraction with spot size ~ 1 nm, camera length 235 mm, mapped with step size of 4 nm. See supplementary information S3 for a description of the ASTAR system.

Studies of the compositional distribution of the NWs were performed using STEM-EELS at a JEOL ARM200F TEM operated at 200kV. This microscope is probe-corrected and equipped with a cold FEG. The data was acquired using GIF Quantum ER imaging filter and an energy resolution of 0.33 eV (measured at the FWHM of the zero loss peak) in dual EELS mode, acquiring low loss and high loss spectra at the same time. For the data treatment we used MLLS fitting algorithm in Gatan Microscopy Suite ® 's Element Quantification tool in order to analyze the signal from the overlapping Co and Ni edges. See supplementary information S4 for a description of the MLLS fitting procedure.

Micromagnetic simulations were performed using OOMMF [START_REF] Donahue | OOMMF User's Guide[END_REF] with the following magnetic parameters: saturation magnetization, Ms-hco = 1273 kAm -1 31 ; exchange constant, Ahcp = 26 x 10 -12 Jm -1 , magnetocrystalline anisotropy, K1hcp = 350 kJm -3 (uniaxial anisotropy, easy axis oriented 78 relative to NW axis). A representative 3D shape of the NW, with diameter of 70 nm, was built by stacking magnetic unit cells of 5 x 5 x 5 nm 3 .

Figure

  Figure 1a displays a TEM image of a representative Co85Ni15 NW of 70 nm diameter. The over-focused Lorentz image depicted in Figure 1b reveals an inhomogeneous magnetic configuration in the stippled region of the NW.

Figure 1 :

 1 Figure 1: (a) BF-TEM image and (b) over-focused Lorentz image of sample NW. (c) Unwrapped magnetic phase shift image of stippled region marked in (a) and (b) with magnetic phase shift in radians represented with color scale, and (d) magnetic flux lines obtained from the cosine of (c) with amplification factor 4. (e) Plot of measured phase shift of cross sections in regions marked by red and gray arrows in (c).

Figure 2 :

 2 Figure 2: Experimental results of structural analysis of nanowire region. (a) Virtual bright field image of scanned nanowire area. (b)-(d) Crystal orientation map showing orientation of [111] and [0001] axis of respectively fcc grains and hcp grains by color code after angular displacement with respect to (b) x (c) y and (d) z axis. (d) Virtual crystal phase map of region in (a), where blue represent highest match for fcc phase, and red for hcp. (f) Superimposed magnetic phase shift image and virtual crystal phase map of the same nanowire region where only the hcp phase regions are visible. (g) The hcp and fcc facets from the orientation color code maps in (b)-(d)

Figure 3 :

 3 Figure 3: Results from micromagnetic simulation. (a) 3D representation of the simulation showing the magnetic vectors with their x-y-direction indicated by the color wheel. Zoomed images of the vortex state displayed below in (a). (b) Magnetic phase image and (c) magnetic flux lines obtained from the simulation.

Figure 4 :

 4 Figure 4: Experimental results of compositional analysis. (a) Bright field image. (b) Magnetic phase shift image of corresponding region. (c) and (d) show compositional maps of respectively Co and Ni composition from squared region in (a).

ACKNOWLEDGMENTS

The research leading to these results has received founding from the European Union Horizon 2020 research and innovation program under grant agreement No. 823717 -ESTEEM3. The authors acknowledge the French National Research Agency under the "Investissement d'Avenir" program reference No. ANR-10-EQPX-38-01 and the "Conseil Regional Midi-Pyrénées" for financial support within the CPER program. This work was also supported by the French national project IODA (ANR-17-CE24-0047) and the international associated laboratory M 2 OZART. This work has been partly supported by the Spanish Ministry of Economy, Industry and Competitiveness (MINECO) under project MAT2016-76824-C3-1-R and by the Regional Government of Madrid under project S2018/NMT-4321 NANOMAGCOST-CM.

ASSOCIATED CONTENT

Supporting Information

Supporting Information accompanies this which gives detailed information about the synthesis of the sample, a basic description of electron holography and of ASTAR, as well as a description of the EELS analysis to separate the Co and Ni edges.

S1: Synthesis of nanowires S2: Electron Holography

S3: ASTAR S4: EELS analysis by MLLS fitting

This material is available free of charge via the Internet at http://pubs.acs.org.

Financial Interest

The authors declare no competing financial interest.

AUTHOR CONTRIBUTIONS