Florian Wasser

Jitae Park

Saicharan Aswartham

Sabine Wurmehl

Yvan Sidis

Paul Steffens

Karin Schmalzl

Bernd Büchner

Markus Braden
email: braden@ph2.uni-koeln.de

F Waßer

J.-T Park

Strong spin resonance mode associated with suppression of soft magnetic ordering in hole-doped Ba1-xNaxFe2As2

Keywords: condensed matter physics, iron-based superconductors, neutron scattering, Na-doped BaFe2As2

INTRODUCTION

Superconductivity (SC) in iron-based superconductors emerges upon suppressing an orthorhombic and antiferromagnetic (o-AFM) state [START_REF] Kamihara | Iron-Based Layered Superconductor La(O1-xFx)FeAs[END_REF][START_REF] Dai | Antiferromagnetic order and spin dynamics in iron-based superconductors[END_REF][START_REF] Hirschfeld | Gap symmetry and structure of Fe-based supersonductors[END_REF] and the highest T c values are realized, when AFM order is completely suppressed and when spin fluctuations are expected to be the strongest. These observations inspired theories with spin-fluctuation-mediated pairing and a SC order parameter that changes sign between the hole and electron pockets of the Fermi surface [START_REF] Hirschfeld | Gap symmetry and structure of Fe-based supersonductors[END_REF]. A hallmark prediction of such theory is a spin exciton appearing below T c at E res < 2∆ SC , with ∆ SC the SC gap energy [START_REF] Hirschfeld | Gap symmetry and structure of Fe-based supersonductors[END_REF][START_REF] Korshunov | Theory of magnetic excitations in iron-based layered superconductors[END_REF][START_REF] Korshunov | Spin resonance peak in Fe-based superconductors with unequal gaps[END_REF]. Experimentally, numerous inelastic neutron scattering (INS) experiments observe spin-resonance modes (SRM) emerging in the SC state at energies below the electron-hole continuum [START_REF] Christianson | Unconventional superconductivity in Ba0.6K0.4Fe2As2 from inelastic neutron scattering[END_REF][START_REF] Inosov | Normal-state spin dynamics and temperature-dependent spin-resonance energy in optimally doped BaFe1.85Co0.15As2[END_REF][START_REF] Zhang | Neutron Scattering Studies of spin excitations in hole-doped Ba 0.67 K 0.33 Fe 2 As 2 superconductor[END_REF][START_REF] Lee | Universality of the Dispersive Spin-Resonance Mode in Superconducting BaFe2As2[END_REF][START_REF] Qureshi | Inelastic Neutron-Scattering Measurements of Incommensurate Magnetic Excitations on Superconducting LiFeAs Single Crystals[END_REF][START_REF] Wang | Strong interplay between stripe spin fluctuations, nematicity and superconductivity in FeSe[END_REF].

In a simple picture the residual magnetic correlations are likely to generate a collective S=1 mode in the SC state, which should be single and isotropic in spin-space, i.e. the magnetic polarization should be identical along all directions. However, polarised INS experiments in Ba(Fe 0.94 Co 0.06 ) 2 As 2 (optimally electron doped) reveal a more complex character [START_REF] Steffens | Splitting of Resonance Excitations in Nearly Optimally Doped Ba(Fe 0.94 Co 0.06 ) 2 As 2 : An Inelastic Neutron Scattering Study with Polarization Analysis[END_REF] by separating the distinct channels in spin space. In addition to a broad SRM that is isotropic and lies at a higher energy corresponding to E res ∼ 5.3k B T c there is a sharp low-energy SRM-1 that is anisotropic in spin space. Qualitatively the same su-perposition of a low-energy anisotropic feature SRM-1 and a broader isotropic one at higher energies, SRM-2, has been established in various FeAs-based superconductors: in Ba(Fe 0.94 Co 0.06 ) 2 As 2 (optimally electron doped) [START_REF] Steffens | Splitting of Resonance Excitations in Nearly Optimally Doped Ba(Fe 0.94 Co 0.06 ) 2 As 2 : An Inelastic Neutron Scattering Study with Polarization Analysis[END_REF][START_REF] Waßer | Anisotropic resonance modes emerging in an antiferromagnetic superconducting state[END_REF], in NaFe 1-x Co x As [START_REF] Zhang | Anisotropic neutron spin resonance in underdoped superconducting NaFe1-xCoxAs[END_REF][START_REF] Song | Temperature and polarization dependence of low-energy magnetic fluctuations in nearlyoptimal-doped[END_REF], in P-doped BaFe 2 As 2 [START_REF] Hu | Spin excitation anisotropy in optimal-isovalentdoped superconductor BaFe[END_REF], in Ni-doped BaFe 2 As 2 [START_REF] Luo | Spin Excitation Anisotropy as a Probe of Orbital Ordering in the Paramagnetic Tetragonal Phase of Superconducting BaFe 1.904 Ni 0.096 As 2[END_REF], and in holedoped BaFe 2 As 2 [START_REF] Zhang | Magnetic anisotropy in hole-doped superconducting Ba 0.67 K 0.33 Fe 2 As 2 probed by polarized inelastic neutron scattering[END_REF][START_REF] Qureshi | Anisotropy of incommensurate magnetic excitations in slightly overdoped Ba0.5K0.5Fe2As2 probed by polarized inelastic neutron scattering experiments[END_REF]. Various attempts were made to attribute the split and anisotropic SRMs to either persisting antiferromagnetic correlations and their corresponding excitations [START_REF] Knolle | Magnetic resonance from the interplay of frustration and superconductivity[END_REF][START_REF] Lv | Double magnetic resonance and spin anisotropy in Fe-based superconductors due to static and fluctuating antiferromagnetic orders[END_REF][START_REF] Wang | Experimental elucidation of the origin of the 'double spin resonances' in Ba(Fe1-xCox) 2 As2[END_REF] or to an orbital-selective pairing [START_REF] Korshunov | Spin resonance peak in Fe-based superconductors with unequal gaps[END_REF][START_REF] Yu | Orbital-selective superconductivity, gap anisotropy, and spin resonance excitations in a multiorbital t -J1 -J2 model for iron pnictides[END_REF]. However, none of these scenarios can account for the existence and the character of the split resonance modes in a large variety of materials extending into the overdoped range [START_REF] Waßer | Anisotropic resonance modes emerging in an antiferromagnetic superconducting state[END_REF][START_REF] Qureshi | Local magnetic anisotropy in BaFe 2 As 2 : A polarized inelastic neutron scattering study[END_REF][START_REF] Wang | Longitudinal Spin Excitations and Magnetic Anisotropy in Antiferromagnetically Ordered BaFe 2 As 2[END_REF]. The spin-space anisotropy must be attributed to finite spin-orbit coupling, whose relevance in iron-based superconductors is documented in the large anisotropy gaps of the magnon dispersion in the o-AFM phase [START_REF] Qureshi | Inelastic Neutron-Scattering Measurements of Incommensurate Magnetic Excitations on Superconducting LiFeAs Single Crystals[END_REF]26], in the splitting of otherwise degenerate electron energy bands [START_REF] Borisenko | Direct observation of spin-orbit coupling in iron-based superconductors[END_REF] and in the spin reorientation transition in hole-underdoped BaFe 2 As 2 that restores tetragonal symmetry [START_REF] Avci | Magnetically driven suppression of nematic order in an iron-based superconductor[END_REF][START_REF] Waßer | Spin reorientation in Ba0.65Na0.35Fe2As2 studied by single-crystal neutron diffraction[END_REF][START_REF] Böhmer | Superconductivityinduced re-entrance of the orthorhombic distortion in Ba1-xKxFe2As2[END_REF][START_REF] Taddei | Detailed magnetic and structural analysis mapping a robust magnetic C4 dome in Sr1-xNaxFe2As2[END_REF][START_REF] Scherer | Spin-Orbit Coupling and Magnetic Anisotropy in Iron-Based Superconductors[END_REF].

Concerning the split SRM's, the two best studied series are both electron doped: Ba(Fe 1-x Co x ) 2 As 2 and NaFe 1-x Co x As [START_REF] Steffens | Splitting of Resonance Excitations in Nearly Optimally Doped Ba(Fe 0.94 Co 0.06 ) 2 As 2 : An Inelastic Neutron Scattering Study with Polarization Analysis[END_REF][START_REF] Waßer | Anisotropic resonance modes emerging in an antiferromagnetic superconducting state[END_REF][START_REF] Zhang | Anisotropic neutron spin resonance in underdoped superconducting NaFe1-xCoxAs[END_REF][START_REF] Song | Temperature and polarization dependence of low-energy magnetic fluctuations in nearlyoptimal-doped[END_REF][START_REF] Wang | Orbital selective neutron spin resonance in underdoped superconducting NaFe0.985Co0.015As[END_REF].

For underdoped Ba(Fe 1-x Co x ) 2 As 2 (x = 4.5 %), nematic and AFM order with sizeable moments precede SC resulting in a large gap in the longitudinal spin fluctuations (polarized along the ordered moment in orthorhombic a direction). In

ℜ * 〈χ ⊥ ' ' 〉 ( µ 2 B / e V ⋅f . u . ) E ( m e V ) L = 1 ( b ) E ( m e V ) o -A F M T ( K ) x B a 1 -x N a x F e 2 A s 2 S C C 4 Figure 1.
Spin resonance modes in the superconducting phases. INS spectra obtained at the AFM Bragg positions (0.5,0.5,L) with L=1,3 for the three samples studied. Data were corrected for background, for the Bose and form factors and normalized to absolute units, see methods section. The spectra were fitted with two log-normal functions corresponding to the two SRM's at 4 and 8-10meV. The inset indicates the location in the phase diagram of Ba1-xNaxFe2As2 for the three samples studied.

consequence only anisotropic resonance modes emerge in the transverse channels [START_REF] Waßer | Anisotropic resonance modes emerging in an antiferromagnetic superconducting state[END_REF], which clearly disagree with the isotropic spin-exciton model [START_REF] Hirschfeld | Gap symmetry and structure of Fe-based supersonductors[END_REF]. At optimal Co doping (x = 6 %), an anisotropic low-energy mode is found in addition to an isotropic one at higher energies [START_REF] Steffens | Splitting of Resonance Excitations in Nearly Optimally Doped Ba(Fe 0.94 Co 0.06 ) 2 As 2 : An Inelastic Neutron Scattering Study with Polarization Analysis[END_REF][START_REF] Waßer | Anisotropic resonance modes emerging in an antiferromagnetic superconducting state[END_REF], while for Ni overdoping (x = 10.9 %) only the isotropic part persists [START_REF] Wang | Experimental elucidation of the origin of the 'double spin resonances' in Ba(Fe1-xCox) 2 As2[END_REF]. In NaFe 1-x Co x As the SRM evolves in a similar way with increasing doping; the intense and anisotropic low-energy part is gradually suppressed following the suppression of the AFM ordering, while the part at higher energies is isotropic throughout the entire SC dome [START_REF] Zhang | Electron doping evolution of the neutron spin resonance in NaFe1-xCoxAs[END_REF].

For hole doped Ba 1-x K x Fe 2 As 2 INS studies were focusing on samples with optimal and overdoped composition [START_REF] Zhang | Neutron Scattering Studies of spin excitations in hole-doped Ba 0.67 K 0.33 Fe 2 As 2 superconductor[END_REF][START_REF] Qureshi | Anisotropy of incommensurate magnetic excitations in slightly overdoped Ba0.5K0.5Fe2As2 probed by polarized inelastic neutron scattering experiments[END_REF][START_REF] Lee | Suppression of spin-exciton state in hole overdoped iron-based superconductors[END_REF][START_REF] Horigane | Spin excitations in hole-overdoped iron-based superconductors[END_REF][37], where AFM order is completely suppressed [START_REF] Böhmer | Superconductivityinduced re-entrance of the orthorhombic distortion in Ba1-xKxFe2As2[END_REF], or on higher energies [START_REF] Murai | Effect of electron correlations on spin excitation bandwidth in Ba0.75K0.25Fe2As2 as seen via time-of-flight inelastic neutron scattering[END_REF]. For holedoped Sr 1-x Na x Fe 2 As 2 only a single very underdoped composition with low T c was studied [START_REF] Guo | Preferred Magnetic Excitations in the Iron-Based Sr1-xNaxFe2As2 Superconductor[END_REF], which revealed only very weak signature of SRM's. In the underdoped hole-doped regime, there is a second magnetic phase appearing in the o-AFM dome at T reo < T N , where the magnetic moments reorient from in-plane towards outof-plane alignment [START_REF] Waßer | Spin reorientation in Ba0.65Na0.35Fe2As2 studied by single-crystal neutron diffraction[END_REF][START_REF] Taddei | Detailed magnetic and structural analysis mapping a robust magnetic C4 dome in Sr1-xNaxFe2As2[END_REF][START_REF] Allred | Tetragonal magnetic phase in Ba1-xKxFe2As2 from xray and neutron diffraction[END_REF], c.f. schematic phase diagram in Fig. 1. For this spin-reoriented phase a magnetic double-k structure has been reported leaving half of the Fe sites non-magnetic [START_REF] Allred | Double-Q spin-density wave in iron arsenide superconductors[END_REF][START_REF] Mallett | Infrared Study of the Spin Reorientation Transition and Its Reversal in the Superconducting State in Underdoped Ba1-xKxFe2As2[END_REF] and tetragonal (C 4 ) symmetry is recovered [START_REF] Böhmer | Superconductivityinduced re-entrance of the orthorhombic distortion in Ba1-xKxFe2As2[END_REF][START_REF] Wang | Complex phase diagram of Ba1-xNaxFe2As2: A multitude of phases striving for the electronic entropy[END_REF]. Following common use in the literature we label this phase as C 4 . Recent studies of the local structure suggest that these C 4 phases with an average tetragonal structure exhibit very strong orthorhombic fluctuations on short length and time scales [START_REF] Frandsen | Local Orthorhombicity in the Magnetic C4 Phase of the Hole-Doped Iron-Arsenide Superconductor Sr1-xNaxFe2As2[END_REF]. In order to access this region where magnetism

ℜ * <χ' ' ⊥ > ( µ 2 B / e V ⋅f . u . ) ( c ) 8 4 . 2 K E ( m e V ) ( d ) 3 1 . 6 K ( e ) 4 7 . 5 K ( f ) 7 0 . 3 K E ( m e V ) [ 4 0 . 2 ; 3 8 . 6 ] K ( g ) ( h ) 8 0 . 2 K ( i ) 1 1 9 . 7 K E ( m e V )
Figure 2. Magnetic excitations at the AFM Bragg positions in the normal state (a)-(i) Magnetic scattering presented in absolute units for the three samples recorded at (0.5,0.5,1) and (0.5,0.5,3) at various temperatures. The NS response is described by a single relaxor function convoluted with the instrumental resolution.

is particularly soft we explored the spin excitations in Ba 1-x Na x Fe 2 As 2 by polarised and unpolarised INS for two slightly underdoped samples x = 0.35 (Na35, T c =26 K) and x = 0.39 (Na39, T c =29 K) and one optimally doped sample with x = 0.4 (Na40, T c =34 K), see methods section. While the two former compounds exhibit magnetic ordering (T N = 70 and 61 K) and the spin reorientation (T reo = 46 and 44.5 K), Na40 does not show any evidence of magnetic ordering. In spite of the minor doping differences these samples exhibit fully different low-energy SRM's while the high-energy SRM varies continuously with doping and T c . This clearly indicates the close connection of the sharp low-energy SRM with persisting magnetic ordering.

RESULTS

Fig. 1 shows our main result comparing the magnetic response in the SC state for the three concentrations Na35, Na39 and Na40, while Fig. 2 compares the magnetic response of these materials at various temperatures in the normal state (NS). Magnetic INS averages the two components of the generalized dynamic magnetic susceptibility, χ (Q, E), perpendicular to the scattering vector, Q. The INS data were corrected for the background, the Bose statistics and higher-order contaminations and transformed into absolute units as described in the methods section. Since the susceptibility can be anisotropic, the signal corresponds to the average of the two perpendicular components convoluted with the resolution function of the instrument, χ ⊥ (Q, E). In agreement with previous INS studies on various electron and hole doped compounds [START_REF] Waßer | Anisotropic resonance modes emerging in an antiferromagnetic superconducting state[END_REF], the magnetic response in the SC state can be described by a SRM-2 at higher energy, ∼8-10 meV, and a sharper SRM-1 at lower energy, ∼4 meV. While the higher SRM-2 varies hardly with the doping, the low-energy SRM-1 exhibits a remarkable doping dependence. In Na35 there is a clear low-energy peak, which turns into the dominating part of the spectrum in Na39. In contrast for slightly higher doping only a low-energy shoulder remains. Since there is little difference in the SC transition temperatures of Na39 and Na40 the different behavior of the low-energy SRM must be attributed to the full suppression of the AFM ordering in Na40. For Na39 magnetic ordering as sensed by neutron diffraction sets in at 60 K and the spin-reorientation transition is found at 44.5 K. In contrast neutron diffraction on Na40 does not yield any evidence for a magnetic transition.

The resonance energies can be extracted from the data in the SC phases, see Fig. 1, and from the difference spectra of SC and NS intensities, see Fig. 3, and are plotted in Fig. 4 (a). The higher SRM-2 at ∼ 10 meV shows a gradual doping dependency and is similarly strong as the SRM in Ba(Fe 0.925 Co 0.075 ) 2 As 2 [START_REF] Inosov | Normal-state spin dynamics and temperature-dependent spin-resonance energy in optimally doped BaFe1.85Co0.15As2[END_REF], thereby supporting a common mechanism for hole and electron doping, see Fig. 3 (a) and (b). In contrast, the strength of SRM-1 at E res,1 ∼ 4 meV strongly varies between the three samples peaking at the end point of AFM order. Furthermore, SRM-1 dominates the difference excitation spectrum in Na39 where it is about twice as intense as SRM-2. The sharp low-energy SRM-1 in Na39 forms the strongest (in absolute units) SRM reported in all iron-based superconductors studied so far.

Since INS only senses the projection of a magnetic signal perpendicular to Q, the comparison of the (0.5,0.5,1) and (0.5,0.5,3) spectra in the SC state indicates that the sharp extra SRM-1 is essentially polarised along the c direction in Na39 [START_REF]The geometry factors, sin 2 (α) for detecting a c polarized signal at (0.5,0.5[END_REF]. This conclusion is corroborated by polarized neutron scattering experiments with Na39, see supplemental materials [46]. The higher SRM-2 lacks c polarisation at an energy transfer of 10 meV but exhibits a strong [1 10]=b component. In contrast the lower SRM-1 has no b contribution again in agreement with numerous observations for the lower SRM in other materials [12-14, 16, 19]. However, SRM-1 is still essentially polarised along the c direction (79(5)% c polarised and 21% [110]=a polarized) although the static magnetism is rotated from a towards c direction [START_REF] Waßer | Spin reorientation in Ba0.65Na0.35Fe2As2 studied by single-crystal neutron diffraction[END_REF][START_REF] Waßer | Spin reorientation transition in Na-doped BaFe2As2 studied by single-crystal neutron diffraction[END_REF]. The rotation of the AFM ordered moment is thus not reflected by a rotation of the polarisation of this sharp extra lowenergy SRM. c polarised extra SRMs are therefore characteristic for the SC phase of FeAs-based materials [12-14, 16, 19, 39], independently on the alignment of their ordered moments.

The exceptional strength of SRM-1 is even larger than what is suggested in Fig. 1 and3. Because the SRM-1 is anisotropic with no component in the [1 10]=b direction, the c component of SRM-1 χ c (Q, E) should be about a factor 2 larger than the average of its components perpendicular to the scattering vector χ ⊥ (Q, E), shown in Fig. 1.

The upper and lower SRM's differ concerning their Q L dependence. Fig. 3 (a-c) displays the intensity difference of SC state and NS for odd (Brillouin zone center) and even (zone boundary) L values; data are corrected for the magnetic form factor and normalized by phonon intensities for Na35, Na39 and Na40 respectively. SRM-1 becomes strongly suppressed at the magnetic zone boundary with the intensity following {1-0.88 cos(π L 2 ) 2 }, while SRM-2 fully preserves its intensity. This difference suggests an enhanced threedimensional character for SRM-1. The dispersion of SRM-1 is traced at intermediate positions, i.e at 1 ≤ L ≤ 2 for Na39 and at 0 ≤ L ≤ 1 for Na35, c.f. Fig. 3 (d) and (e) respectively. Moreover, the resulting data points for Na35 and Na39 were combined to fit the dispersion of SRM-1 by

E(L) = ∆ + B • sin L-1
2 π , with bandwidth B = 3.2 meV. Despite their different polarisations, peak energies and dimensional character, the dispersion of SRM-1 and SRM-2 is described by the same bandwidth, which is similar to the one found in underdoped Ba(Fe 1-x Co x ) 2 As 2 for x = 4.7 % [START_REF] Pratt | Dispersion of the superconducting spin resonance in underdoped and antiferromagnetic BaFe 2 As 2[END_REF] and which is in agreement with the universal dispersion relation B/k B T c [START_REF] Lee | Universality of the Dispersive Spin-Resonance Mode in Superconducting BaFe2As2[END_REF]. The strong Q L dependence of the SRM-1 intensity is another property of this mode that is difficult to explain in the simple spin-exciton scenario.

The spectra in the SC state exhibit a spin gap, which can be described by the log-normal functions. In contrast all NS spectra can be reasonably well described by the single relaxor formula χ (Q, E) = χ (Q, 0) ΓE Γ 2 +E 2 , see Fig. 2, that is expected for a paramagnetic itinerant magnetic system. This might appear astonishing, as Na35 and Na39 enter the SC state from an AFM ordered phase with essentially c-aligned magnetic moments. For an ordered material one may expect spin gaps arising from anisotropy, as it was reported for the parent compound [START_REF] Qureshi | Local magnetic anisotropy in BaFe 2 As 2 : A polarized inelastic neutron scattering study[END_REF][START_REF] Wang | Longitudinal Spin Excitations and Magnetic Anisotropy in Antiferromagnetically Ordered BaFe 2 As 2[END_REF]. However, in Na35 and Na39 the ordered moments are heavily reduced with respect to undoped BaFe 2 As 2 . In contrast to electron-doped Ba(Fe 0.955 Co 0.045 ) 2 As 2 [START_REF] Waßer | Anisotropic resonance modes emerging in an antiferromagnetic superconducting state[END_REF] the AFM order in these holedoped compounds appears much softer; there is no evidence for a gap in any of the channels in the normal conducting AFM phases. In Na39 just above T c there is little evidence for an anisotropy between c and a polarised excitations, see Fig. 2 (d), while in Na35 the c axis response is slightly suppressed, see Fig. 2 (a), as it is expected for AFM ordering with moments along c, and as it was also reported for very underdoped Sr 1-x Na x Fe 2 As 2 only [START_REF] Guo | Preferred Magnetic Excitations in the Iron-Based Sr1-xNaxFe2As2 Superconductor[END_REF]. Again this suggests that the AFM ordered moment and its directional pinning in Na39 is too small to significantly impact the inelastic magnetic response, see also below. The difference between the two stronger doped compounds and Na35 is also seen when tracing the single-relaxor parameters against temperature in the NS, see Fig. 4 (c,d). For the inverse of the amplitude,

1 χ (Q,0) , a linear temperature dependency corresponding a Curie-Weiss law, χ (Q, 0) ∝ 1
T -Θ , can be expected [START_REF] Steffens | Magnetic excitations in the metallic single-layer ruthenates Ca2-xSrxRuO4 studied by inelastic neutron scattering[END_REF], which indeed is roughly fulfilled in both compounds with identical slope and Weiss temperature Θ=22 K. In contrast the AFM ordering in Na35 results in qualitatively different temperature dependencies. Also the plot of the characteristic energy, Γ, indicates the different behavior of Na35 and Na39/Na40. The latter two samples show a similar temperature dependency that most interestingly is very close to the Planck scaling for the characteristic energy, Γ = k B T [START_REF] Zaanen | Why the temperature is high[END_REF], indicated by the blue bar.

Further insight into the character of the SRMs can be obtained by comparing the temperature dependencies of the inelastic signals with those of the elastic Bragg intensities for the three compositions, see Fig. 5. The elastic signals measured on the same crystals were taken from references [START_REF] Waßer | Spin reorientation in Ba0.65Na0.35Fe2As2 studied by single-crystal neutron diffraction[END_REF][START_REF] Waßer | Spin reorientation transition in Na-doped BaFe2As2 studied by single-crystal neutron diffraction[END_REF]. For all three materials there is a clear suppression of the magnetic signal at 2 meV in the SC phase resulting from the opening of the gap. While in Na40 this 2 meV signal is the strongest just above T c it is already suppressed through the AFM ordering in Na35 and Na39. At (0.5 0.5 1) the 2 meV signal essentially corresponds to c polarised magnetic excitations, which are little influenced by the upper magnetic transition into the o-AFM phase with moments aligned in-plane. The fact that the signal further increases upon cooling in the AFM state corroborates the softer character of the magnetism in these hole-doped materials compared to electron doping [START_REF] Waßer | Anisotropic resonance modes emerging in an antiferromagnetic superconducting state[END_REF]. The maximum 2 meV signal is observed just above the reorientation transition. A continuous rotation of the moments would even require complete softening and divergence of this susceptibility. In the C 4 phase the c polarised excitations become the longitudinal ones, for which strong suppression is expected. Note, however, that in the double-q magnetic structure with moments pointing along c, half of the Fe sites exhibit zero magnetic moment, which can result in strong c-polarized fluctuations. The magnetic signals near the energies of the two SRMs spontaneously increase in the SC phase. The most remarkable upturn is observed for the low-energy signals in the two materials with coexisting AFM order, Na35 and Na39, underlining that SRM-1 emerges with the opening of the SC gap. This enormous increase of inelastic intensity is accompanied by the partial suppression of the magnetic Bragg intensity and thus by the suppression of ordered magnetic moment described in reference [START_REF] Waßer | Spin reorientation transition in Na-doped BaFe2As2 studied by single-crystal neutron diffraction[END_REF]. The by far strongest increase of SRM scattering in the SC state is found in Na39 where it is accompanied by the most pronounced drop of static intensity suggesting that the SRM is closely related with the suppressed magnetic moment, as it will be quantitatively analyzed below.

DISCUSSION

The comparison of the three samples with little variation of the Na doping gives a detailed insight in the character and origin of the split SRMs appearing in various FeAs-based superconductors. Compared to the electron doped phase diagrams the AFM ordering in the hole-doped series seems to be softer. While the anisotropy gaps in the electron-doped compounds are sizeable and thus effectively pin the ordered moment to lie parallel to the FeAs layers [START_REF] Waßer | Anisotropic resonance modes emerging in an antiferromagnetic superconducting state[END_REF], no such gaps are visible in the magnetic response of the two Na doped BaFe 2 As 2 compounds that exhibit magnetic order and the spinreorientation transition, Na35 and Na39. For hole doping at temperatures just above the SC transition, there is thus much more spectral weight situated at low energies, which might be the clue to understand the higher SC transition temperatures in hole versus electron doped compounds.

In spite of the spin-reorientation transition the magnetic excitations in SC Ba 1-x Na x Fe 2 As 2 , i.e. the SRMs, qualitatively resemble those in electron doped compounds. There is a clear superposition of at least two SRMs with similar energy dispersion along L, from which the upper possesses a two-dimensional and the lower one a three-dimensional character. Most remarkably the lower SRM-1 exhibits qualitatively the same anisotropy with a predominant c polarized character as previously observed in materials with a aligned magnetism. The anisotropy of the SRM-1 thus does not follow the spin re-Table I. Quantitative comparison of the static and dynamic signals for the three compounds Na35, Na39 and Na40 calculated by integrating the static and inelastic neutron scattering response, for precise temperatures see caption of Fig. 3. All quantities are given in Bohr magnetons squared, µ 2 B and fluctuating moments correspond to the sum of the directions. µ 2 SRM-1 and µ 2 SRM-2 give the total squared moment in the two resonance modes integrated up to 20 meV; µ 2 NS the fluctuating moments in the NS; ∆µ 2 stat is the reduction of ordered moment squared upon entering the SC state. There is some ongoing debate whether the resonance excitations can also be explained within the s ++ orbital fluctuations scenario. However, the low energy of only ∼4 meV for the lower SRM-1, which without any doubt emerges in the SC state, rules out such an explanation for this mode. Its energy is clearly below twice the sum of a smaller and a larger gap for all three materials studied, which was formulated as a strict criterion for s± pairing by Korshunov et al. [START_REF] Korshunov | Spin resonance peak in Fe-based superconductors with unequal gaps[END_REF].

µ 2 [µ 2 B ] Na35 Na39 Na40 µ 2 SRM-
The soft AFM ordering and the stronger coupling between SC and the c-aligned order seem to be the cause of the exceptionally strong SRM-1 appearing for the Na content closest to the doping-induced full suppression of magnetic order. This strong inelastic mode, whose peak amplitude is the strongest one reported for any FeAsbased SC so far, is accompanied by the pronounced suppression of the ordered c-polarized moment upon entering the SC state. In order to quantify this relation between inelastic and elastic signals, the energy and Q-integrated strength of SRM-1 as well as those of SRM-2 and of the NS response can be calculated from the signal in absolute units. Since we are interested in temperature differences and since there seems to be no impact of SC at high energies, we average the generalized susceptibility over Q in a Brillouin zone and integrate it over energy from 0 to 20 meV, see methods section and [46]. These calculations take the geometry factors of the signals and the Q L dispersion of the amplitudes and peak energies of the two SRM's into account, and the results are resumed in table I.

Although the lower SRM-1 exhibits by far the largest peak amplitude its total fluctuating moment is much smaller than that of SRM-2, because it looses rapidly its weight when L varies away from the odd zone-center values, see Fig. 3, in addition it essentially concerns only one spin direction while SRM-2 is isotropic. Furthermore, in the description of the SC response by two log-normal functions the upper one contains also the part of the spectrum that does not change upon entering the SC state yielding its much larger total weight. These fluctuating moments can be compared to the reduction of the ordered moment squared obtained from the magnetic Bragg scattering, see [46]. For Na35 the ordered moment decreases from 0.222 to 0.208 µ B and for Na39 from 0.189 to 0.155, which corresponds to a sizeable reduction of the square of the ordered moment, see table I. Indeed the total fluctuating moment of SRM-1 quantitatively follows the reduction of the ordered moment squared. There is also a clear total enhancement of magnetic fluctuations in the SC state, which points to a significant gain in exchange energy similar to other unconventional superconductors [51,[START_REF]The exchange energy can be estimated within the Heisenberg model[END_REF].

The good agreement between the suppressed magnetic order and the strength of SRM-1 for the two compounds with coexistence of SC and AFM order suggests that the SRM-1 is related to the suppression of magnetic order. The fact that SRM-1 is essentially c polarized nicely agrees with the observation that c-ordered magnetism competes more strongly with SC or becomes more strongly suppressed [START_REF] Böhmer | Superconductivityinduced re-entrance of the orthorhombic distortion in Ba1-xKxFe2As2[END_REF][START_REF] Waßer | Spin reorientation transition in Na-doped BaFe2As2 studied by single-crystal neutron diffraction[END_REF]. For Na40, which does not exhibit any AFM ordering, the weight of SRM-1 can stem from the suppression of anisotropic low-energy fluctuations in the normal and paramagnetic state, see Fig. 2. In view of the observation of a qualitatively similar mode at almost the same energy of ∼4 meV in so many different compounds [START_REF] Steffens | Splitting of Resonance Excitations in Nearly Optimally Doped Ba(Fe 0.94 Co 0.06 ) 2 As 2 : An Inelastic Neutron Scattering Study with Polarization Analysis[END_REF][START_REF] Zhang | Anisotropic neutron spin resonance in underdoped superconducting NaFe1-xCoxAs[END_REF][START_REF] Zhang | Magnetic anisotropy in hole-doped superconducting Ba 0.67 K 0.33 Fe 2 As 2 probed by polarized inelastic neutron scattering[END_REF][START_REF] Qureshi | Anisotropy of incommensurate magnetic excitations in slightly overdoped Ba0.5K0.5Fe2As2 probed by polarized inelastic neutron scattering experiments[END_REF] there must be an intrinsic cause for it basing on the AFM or nearly AFM band structure. The spin reorientation seems not to have a qualitative impact on this mode but the c aligned magnetic order couples more strongly with SC and thus yields a stronger SRM-1.

The coexistence of AFM order and SC has been too little studied in theory, just for the case of a single band and without spin-orbit coupling it was found that transverse excitations should remain ungapped and that the longitudinal channel develops a resonance [START_REF] Ismer | Magnetic Resonance in the Spin Excitation Spectrum of Electron-Doped Cuprate Superconductors[END_REF][START_REF] Rowe | Spin excitations in layered antiferromagnetic metals and superconductors[END_REF]. This longitudinal resonance might be related to the peculiar behavior of SRM-1.

In summary there are three properties of the lower SRM in Na-doped BaFe 2 As 2 that challenge the mostly accepted exciton picture. Firstly the split SRMs partially share the same polarization while there should only exist a single bound state below the electron-hole continuum. Secondly, the amplitude of the lower SRM exhibits a strong Q L dependence in contrast to the highly twodimensional electron band structure well reflected by the high energy SRM. And thirdly, the lower SRM sharply peaks at the suppression of the AFM ordering, while the exciton intensity should be determined essentially by the distance to the continuum, which in Na-doped BaFe 2 As 2 cannot vary so sharply. Furthermore this exceptionally strong SRM-1 in Na39 exhibits the same polarization as previously observed in electron doped systems in spite of the spin reorientation. The stronger competition between c aligned magnetic order and SC in this hole-doped material seems to imply the strong low-energy anisotropic SRM.

METHODS

Ba 1-x Na x Fe 2 As 2 single crystals were synthesised by a self-flux method as described in Ref. [START_REF] Aswartham | Hole doping in BaFe2As2: The case of Ba1-xNaxFe2As2 single crystals[END_REF]. Thereby we obtained samples with x = 0.35 (Na35) and m = 294 mg, x = 0.39 (Na39) and m = 172 mg and x = 0.40 (Na40) and m = 42 mg. The high sample quality was assessed by EDX, magnetisation and transport measurements [START_REF] Aswartham | Hole doping in BaFe2As2: The case of Ba1-xNaxFe2As2 single crystals[END_REF] as well as neutron scattering [START_REF] Waßer | Spin reorientation in Ba0.65Na0.35Fe2As2 studied by single-crystal neutron diffraction[END_REF][START_REF] Waßer | Spin reorientation transition in Na-doped BaFe2As2 studied by single-crystal neutron diffraction[END_REF]. Note that there is some discrepancy between various phase diagrams reported for Ba 1-x Na x Fe 2 As 2 [START_REF] Waßer | Spin reorientation transition in Na-doped BaFe2As2 studied by single-crystal neutron diffraction[END_REF]; here we label the crystals according to their Na content as determined by the EDX measurements. The single crystals were air-tightly sealed in thin Al cans containing Ar atmosphere in order to prevent potential degradation in air. Unpolarised INS experiments were performed at the thermal triple-axis-spectrometer (TAS) PUMA at Meier-Leibnitz Zentrum in Garching, Germany, and at the cold TAS 4F1 at the Laboratoire Léon Brillouin in Saclay, France. Polarised INS experiments were conducted at the thermal TAS IN22 at Institut Laue Langevin in Grenoble, France, where polarised neutrons were generated and analysed via a Heusler-monochromator andanalysor, respectively, see the supplemental material [46]. Each instrument was operated in constant-k f mode and k f was fixed to 2.662 Å-1 in conjunction with a pyrolytic graphite (PG) filter in case of thermal TAS and to 1.55 Å-1 in conjunction with a cooled beryllium filter in case of cold TAS.

The samples were aligned within the [1, 1, 0]/[0, 0, 1] scattering geometry corresponding to orthorhombic a and c directions. Throughout this paper we use the tetragonal notation and denote the scattering vector Q in reciprocal lattice units. Whenever possible, the background was determined by rotating the sample, fitted and subtracted from the data, see supplemental material [46]. Furthermore, corrections for the thermal population (Bose factor) and the energy dependent fraction of higher-order neutrons (monitor factor) were applied. For consistency two symmetry-equivalent Q positions at (0.5, 0.5, 1) and (0.5, 0.5, 3) were probed by series of Escans (constant Q) and Q-scans (constant E).

The intensities in INS correspond to the doubledifferential cross section, d 2 σ dΩdE , scaled with the flux and with the transmission factor and convoluted with the resolution function of the spectrometer. We followed the approach described in reference [START_REF] Qureshi | Fine structure of the incommensurate antiferromagnetic fluctuations in single-crystalline LiFeAs studied by inelastic neutron scattering[END_REF] to convert the energy spectra in Fig. 2 to an absolute scale by normalizing through phonon scattering [46] and estimating the resolution of PUMA spectrometer by the Reslib-code [START_REF] Zheludev | Manual: ResLib 3.4. Neutron Scattering Sciences Division[END_REF]. Note, however, that the folding with the resolution function is nontrivial so that this normalized INS signal corresponds to the double-differential cross section only when the resolution is better than the typical variation of the cross section with the scattering vector, Q, or energy transfer, E. This condition is not always fulfilled for the magnetic response in FeAs-based SC's. The double differential cross section is given by the imaginary part of the generalized dynamic susceptibility:

d 2 σ dΩdE = γr 0 2 2 • k f k i • N πµ 2 B • e -2W (Q) 1 -e -E k B T × f 2 (Q) • χ (Q, E)× α,β δ αβ - Q α • Q β |Q| 2 , (1)
where α,β δ αβ -Q α • Q β /|Q| 2 corresponds to a factor two for isotropic magnetic signals and to the average of the two components perpendicular to Q in an anisotropic case. The data were corrected for this geometry factor yielding the average of the two perpendicular components of χ (Q, E), χ ⊥ (Q, E) . The fact that the signal still contains the resolution folding is reflected by the label χ ⊥ (Q, E) in Figures 1, 2 ln(E res,j ) -ln(E) w j 2 was used, that were previously shown to well describe SC magnetic excitations in Fe-based SC's [START_REF] Waßer | Anisotropic resonance modes emerging in an antiferromagnetic superconducting state[END_REF][START_REF] Wang | Experimental elucidation of the origin of the 'double spin resonances' in Ba(Fe1-xCox) 2 As2[END_REF][START_REF] Tucker | Crossover from spin waves to diffusive spin excitations in underdoped Ba(Fe1-xCox)2As2[END_REF]. In contrast the NS response is described by a single relaxor function χ (Q, E) = χ (Q, 0)

• Γ•E Γ 2 +E 2 .
For the calculation of the fluctuating moments the Q dependence was described by exp(-0.5( h-0.5 w hk ) 2 )exp(-0.5( k-0.5 w hk ) 2 ) with a constant width that corresponds to a half width at half maximum of 0.027 reciprocal lattice units in (hhL) scans, see also [46]. The dispersion of the resonance energies as well as that of the amplitude of SRM-1 was described by the formulas given in the RESULTS section. The parameters shown in Fig. 4 (averaged for L=1 and 3) were used and the width parameters of SRM-1(SRM-2), w 1,2 , are 0.151(0.670), 0.151(0.532), 0.151(0.330) for Na35, Na39 and Na40, respectively. For the anisotropic SRM-1 a geometry factor of 1.5 was applied, while for the isotropic signals the three directions were summed up. Note that error bars in all figures correspond to the standard deviation of the intensity and do not include errors of the normalization process, which would be in the range of ∼20 % [START_REF] Xu | Absolute crosssection normalization of magnetic neutron scattering data[END_REF].

Figure 3 .

 3 Figure 3. Dispersion of the resonance modes. (a)-(c) Normalized intensity difference of the SC state and NS at odd and even L-values for Na35, Na39 and Na40, respectively. Solid lines are (asymmetric, i.e. different widths above and below the peak) Gaussians peaking at different energies for odd respectively even L-values. Data in the SC state was taken at 3.5 K, and data in the NS at 38 and 32 K for Na35 and Na39, respectively, and at 39 and 40 K for L=1 and 3 with Na40. (d) Lower part of the split spin resonance mode for 1 ≤ L ≤ 2 of Na39 displays a dispersion to higher energies and a reduction in intensity. (e) Same as in (d) but for Na35 at 0 ≤ L ≤ 1. (f ) Fit of the dispersion as described in the main text in which the data points of Na35 and Na39 were combined. Disregarding the color, all triangular symbols belong to Na35, while all spherical symbols belong to Na39.

  -2 f r o m d i f f .

Figure 4 .

 4 Figure 4. Energies and amplitudes of magnetic scattering. Parameters describing the magnetic response obtained from the spectra and difference spectra. (a) and (b)show the energies and the amplitudes of the SRM-1 and SRM-2 log-normal functions plotted against the Tc of the three samples studied. For the high-energy SRM-2 we include the value obtained from fitting the intensity differences shown in Fig.3(black squares). (c) and (d) resume the single-relaxor parameters describing the normal-state response traced against the temperature. One recognizes that Na39 and Na40 behave very similarly concerning both the amplitude and the characteristic energies, while the response of Na35 is determined by the stronger static AFM order. The linear fit in (c) corresponds to a Curie-Weiss law, and the blue bar in (d) denotes the Planck scaling Γ = kBT .

Figure 5 .

 5 Figure 5. Temperature dependence of the elastic and inelastic response. (a)The temperature dependent scattering of the (0.5, 0.5, 1) magnetic Bragg peak of Na35 shows the three phase transitions, data taken from[START_REF] Waßer | Spin reorientation in Ba0.65Na0.35Fe2As2 studied by single-crystal neutron diffraction[END_REF] and binned within 1 K. (b) Inelastic response of Na35 displays a peak for 2 meV at Treo, while the intensity uptake at 5 meV and 12 meV corresponds to the formation of the resonance mode. (c) Elastic response of Na39 determined at the (0.5, 0.5, L) positions that sense c and a polarized moments differently[START_REF]The geometry factors, sin 2 (α) for detecting a c polarized signal at (0.5,0.5[END_REF], data taken from[START_REF] Waßer | Spin reorientation transition in Na-doped BaFe2As2 studied by single-crystal neutron diffraction[END_REF]. (d) Inelastic response of Na39 at (0.5, 0.5, 1) showing for 2 meV a maximum at Treo and a suppression in the SC phase. The emergence of the SRM's result in increasing intensities at 4 meV and 10 meV below Tc. (e) The constant elastic scattering at the (0.5, 0.5, 1) magnetic Bragg-position for Na40 shows the absence of magnetic ordering down to the lowest temperatures, data taken from[START_REF] Waßer | Spin reorientation transition in Na-doped BaFe2As2 studied by single-crystal neutron diffraction[END_REF]. (f ) Inelastic response of Na40 showing a maximum for 2 meV at Tc and an intensity uptake due to the SRM formation at 6 meV and 11 meV, respectively. All lines are guides to the eye and the colored backgrounds correspond to the SC, C4 and o-AFM phases.

and 5 .

 5 The lines in Figures1 and 2are a fit of a model of χ (Q, E) convoluted with the instrumental resolution. For the split SRMs a phenomenological model of two (j = 1, 2) log-normal functionsL j (E) = A j (2π)w j E exp -1 2

ACKNOWLEDGEMENTS

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through the Priority Programme SPP1458 (BE1749/13, BU887/15-1 and BR2211/1-1). S. W. thanks the DFG for funding in the Emmy Noether programme (WU595/3-3).

DATA AVAILABILITY

All relevant data that support the findings of this study are available from the corresponding author on request.

COMPETING INTERESTS

The authors declare no competing interests.


Johannes Fuchs
email: fuchs@dbvis.inf.uni-konstanz.de

Petra Isenberg
email: pe-tra.isenberg@inria.fr.

Anastasia Bezerianos
email: anastasia.bezerianos@lri.fr.

Matthias Miller
email: miller@dbvis.inf.uni-konstanz.de

Daniel A Keim
email: keim@uni-konstanz.de

Teaching Clustering Algorithms with EduClust: Experience Report and Future Directions

We share our experiences teaching university students about clustering algorithms using EduClust, an online visualization we developed. EduClust supports professors in preparing teaching material and students in visually and interactively exploring cluster steps and the effects of changing clustering parameters. We used EduClust for two years in our computer science lectures on clustering algorithms and share our experience integrating the online application in a data science curriculum. We also point to opportunities for future development.

Introduction

We are currently seeing an immense increase in online learning platforms and sharing of teaching material [START_REF] Allen | Changing course: Ten years of tracking online education in the United States[END_REF]. We implemented EduClust (Fig. 2) to reduce the considerable effort in creating high quality teaching material and to encourage learning in-and outside the classroom. EduClust is an easily accessible online visualization application, which supports dynamic teaching and learning of clustering algorithms [START_REF] Fuchs | Educlust-a visualization application for teaching clustering algorithms[END_REF]. Simple two-dimensional data representations like scatterplots are used to show clustering behavior. We added animations to communicate changes between algorithmic steps. Different algorithms can be applied to various datasets and can be steered by changing input parameters or distance metrics. Additionally, further details about the algorithms are provided in a separate panel showing pseudo code, algorithmic complexity, and hyper parameters.

Computer Graphics and Applications

For two years we used EduClust in our teaching routine. Based on our experiences with the software we provide the interested reader with some guidance on preparing and organizing teaching material (e.g., slides and assignments) together with ideas about how to include the software in classroom settings (e.g., hands-on sessions with students). Given the positive feedback from our students using the software, we want to motivate similar development and research in this area.

Teaching Scenarios with EduClust

EduClust is accessible online (http://educlust. dbvis.de/) and comes with nine different clustering implementations and an initial pool of datasets. Teachers and students can start right away using the software. In our data mining lecture at the University of Konstanz, we teach several different clustering algorithms. Our learning goals are based on Krathwohl's revised version of Bloom's educational objectives [START_REF] Krathwohl | A revision of bloom's taxonomy: An overview[END_REF]. They comprise simple cognitive processes like remembering which clustering algorithms exist and understanding the different categories the algorithms fall into, as well as the single steps of the algorithmic behavior. We want students to be able to apply the clustering algorithms to data in a meaningful way and analyze the influence of input parameters, or distance measures on the clustering result. Ultimately we want students to evaluate (see Fig. 1) the performance of clustering algorithms in certain situations and create scenarios, in which algorithms fail or outperform others. With EduClust, we were able to teach even complex cognitive processes and reduce the preparation time of the lecturer to a minimum. With EduClust, one can use an export mechanism for individual clustering animations and the details about the algorithm provided in the information space. Lecturers just have to decide which algorithms, hyper parameters, and datasets they want to include in the slide deck. They run the software once and export the displayed animations in graphics interchange format (gif) to use in their slides. For details about the algorithmic behavior, complexity, or input parameters EduClust provides ample text that can be copied on slides as well.

During the Lecture

To profit from EduClust during the lecture, we found it useful to split the session into three parts. First, a theoretical introduction to a new algorithm; next, a hands-on session; and finally a group discussion of advantages and disadvantages of different algorithms.

In our lectures, we always introduce new clustering algorithms showing slides with text information and pseudo code first, followed by a moderated animation generated by EduClust Fig. 3. Students can see the algorithm in action, understand the individual clustering steps and relate to the previously shown text descriptions. This first introduction is meant to support the cognitive processes remember and understand.

In the second part of the lecture, students use EduClust on their own to apply the algorithms to different datasets and analyze their peculiarity. Students, thus, experience the influence of changing input parameters and cluster characteristics. The duration of this individual hands-on sessions depends on the complexity of the algorithm.

In the third part, we put clustering algorithms into context with each other (Fig. 1). The lecturer starts a discussion by bringing up a dataset with specific characteristics. Students then discuss whether or not clustering algorithms are capable of separating data points into clusters. The lecturer and students use EduClust to try algorithms with various input parameters and discuss their advantages and disadvantages. Thereby, students evaluate the usefulness of algorithms and understand their individual application areas.

We found that this lecture structure covers nearly all cognitive processes to support student learning. However, we recommend to accompany the session with an assignment sheet to also support create as another cognitive process.

Preparing an Assignment

Our assignments are designed to generate a deep engagement with specific clustering processes. We ask questions that require students to apply algorithms, analyze the consequences when changing input parameters or evaluate different clustering techniques given a certain dataset. To further increase the learning rate, we also include questions, in which students have to create datasets being suitable for the one algorithm but not for the others. In such scenarios, students have to understand details of the algorithms to come to a solution. Trial and error usually fails due to the complexity of the problem space with many different variables e. g., input parameters, clustering algorithms, or distance metrics.

Student Assessment

EduClust supports the export and import of data files in json format. This feature can facilitate the correction of submissions. When students have to create datasets for their assignment, they can export them and email their result to the lecturer. The lecturer can use EduClust to import the dataset and check for correctness.

Summary of Benefits

Although not exhaustive, EduClust covers the most prominent clustering algorithms and provides a visual categorization based on their clustering behavior. Lecturers can do live demonstrations of the clustering behavior of individual algorithms and use EduClust to prepare teaching material. EduClust offers datasets covering various cluster characteristics, which can be used together with all implemented clustering algorithms. The influence and importance of choosing input parameters wisely can be shown by running the same algorithm on the same dataset with varying input parameters. During the lecture, multiple clustering algorithms can be compared using the same dataset, revealing the benefits of each clustering algorithm. Both the description of algorithmic steps (in text), and a sequence of images showing these steps on a dataset, can be exported and added to traditional teaching material.

Students can apply clustering algorithms without implementation effort to various datasets and rerun the same algorithm multiple times using different input parameters. While running the algorithm, the underlying pseudo code is displayed in the information space. The selection of different algorithms and datasets help students to evaluate the performance of the respective algorithms. Finally, students can create individual datasets to be clustered with all implemented algorithms.

Future Research Directions

Qualitative evaluations showed that students are willing to use EduClust in their learning routine [START_REF] Fuchs | Educlust-a visualization application for teaching clustering algorithms[END_REF]. Currently, EduClust is limited to nine clustering algorithms but we will extend it to include cluster quality measures and additional algorithms like DENCLUE.

Given the positive feedback from our students, we also see a lot of potential for applying what we learned to different categories of algorithms.

A promising starting point could be decision trees. In addition, we would like to use EduClust as a motivation to establish a new research direction called teachable AI. While explainable AI gets a lot of research attention, respective applications focus on understanding the algorithmic behavior of individual architectures. We would like to argue for further research towards experiencing the entire inner workings of multiple algorithms together with the consequences of changing parameters and the possibility to evaluate different approaches on the same dataset, along the lines of explAIner [START_REF] Spinner | explainer: A visual analytics framework for interactive and explainable machine learning[END_REF] but with a focus on teaching ML algorithms from a professor and a student perspective.

Figure 1 :

 1 Figure 1: Four of the nine clustering algorithms and their visualization supported in EduClust: a) k-means clustering centers shown as circles. Shapes in this artificial dataset are not separated well. b) In Single Linkage a dendrogram from the hierarchical clustering (not shown here) was used to determine the effective horizontal cut to differentiate each shape. c) The DBSCAN algorithm uses an ε-distance which is represented using blurry circles. d) The visualization shows the spanning tree of the OPTICS algorithm.

Figure 2 :

 2 Figure 2: Application overview: algorithms and data sets can be selected in the Selection Menu (top), parameters and animations can be adjusted in the Navigation Area and Parameter Settings (left), detailed text descriptions are displayed in the Information Space (right), and the clustering behavior is visualized in the Cluster View (center).

Figure 3 :

 3 Figure 3: Our instructional material consists of three parts: first, introduction slides with pseudo code, second, a live demonstration of the clustering behavior (animations exported with EduClust), third, an evaluation of the clustering results using data sets with different characteristics (in-class exploration with EduClust).

Published by the IEEE Computer Society © 2020 IEEE

May/June 2020

Computer Graphics and Applications


Elodie Vintrou

Valentine Lebourgeois

Agnès Bégué

Dino Ienco

Maguelonne Teisseire

Stéphane Dupuy

Fidiniaina Ramahandry

Identifying cropped areas in small growers agricultural regions using data mining for food security

come

IDENTIFYING CROPPED AREAS IN SMALL GROWERS AGRICULTURAL REGIONS USING DATA MINING FOR FOOD SECURITY

Vintrou Elodie (1) , Lebourgeois Valentine (2) , Bégué Agnès (2) , Ienco Dino (3) , Teisseire Maguelonne (3) , Dupuy Stéphane (2) , Ramahandry Andriandrahona Fidiniaina (4) (1) CIRAD UR AIDA, Station Ligne Paradis, 7 chemin de l'Irat, 97410 Saint Pierre, La Réunion, France Email : elodie.vintrou@cirad.fr (2) CIRAD UMR TETIS, Maison de la Télédétection, 500 rue J.F. Breton, Montpellier, France Email : valentine.lebourgeois@cirad.fr; agnes.begue@cirad.fr (3) IRSTEA UMR TETIS, Maison de la Télédétection, 500 rue J.F. Breton, Montpellier, France Email : teisseire@irstea.fr ; ienco@irstea.fr (4) FOFIFA, Station Régionale de Recherche FOFIFA Tsivatrinikamo ANTSIRABE 110, Madagascar

ABSTRACT

The present study aimed at testing the potential of the future mission SENTINEL-2 (European Copernicus program) to map croplands in a region of Madagascar characterized by small size fields and frequent cloud covering. Two approaches were tested and compared : i) a classical remote sensing method (RS) using image object-based analysis, expert rules and supervised classification, and ii) a data mining (DM) approach consisting of the extraction of frequent patterns from the database and the use of these patterns in different algorithms (Naive Bayes, Random Forest, Decision Tree and Support Vector Machine) to build classification rules. Both methods used SPOT images and a ground data set of 324 GPS waypoints collected during the 2012-2013 cropping season. The remote sensing and data mining approaches showed equivalent overall accuracies (82% vs 84% for RS and DM methods respectively). However, the DM approach showed its ability to handle a large volume of data and to do so in a timely manner. This approach has also the advantage to extract all the information at its disposal, even temporal behaviors, unlike the object-based RS approach which requires significant participation of the expert. Data mining tools are thus recommended for their considerable potential for the classification without a priori of remotely sensed data, mixing multisource information and consequent time series, especially for the upcoming Sentinel-2 images that are expected to generate a large volume of data to store and process.

INTRODUCTION

Food insecurity is particularly worrying in Africa, where nearly one country in four suffers from hunger [START_REF] Fao | the state of food insecurity in the world 2012: Economic growth is necessary but not sufficient to accelerate reduction of hunger and malnutrition[END_REF][START_REF]Statistical yearbook 2013: World food and agriculture[END_REF]. In front of the growing number of natural disasters, the increasing population, the emergence of dedicated crops to production of biofuels, land grabbing by foreign investors etc., there is a need for systematic and accurate monitoring of agricultural systems and their adaptation to changing environment, to assess the impacts on food security. Early warning systems are designed to provide reliable information on preventive potential risk of a food crisis: estimating production is capital to compensate for the lack of food per food aid or imports in developing countries. For that purpose, data on cultivated surfaces and yields are an essential prerequisite for a good agricultural production forecast [START_REF] Brown | Famine early warning systems and remote sensing data[END_REF]. So far, low and moderate resolution satellite remote-sensing images have been extensively used for crop mapping and monitoring [START_REF] Doraiswamy | Application of modis derived parameters for regional crop yield assessment[END_REF][START_REF] Herold | Some challenges in global land cover mapping: An assessment of agreement and accuracy in existing 1 km datasets[END_REF][START_REF] Vintrou | Crop area mapping in west africa using landscape stratification of modis time series and comparison with existing global land products[END_REF]. Their high temporal frequency and their extended geographical coverage associated with free or low costs per area unit makes them a particularly appropriate information source at both national and regional scales. However, with these data, the estimation of cultivated surfaces and the discrimination between different crops is still challenging in countries with fragmented farmland, small size fields or with specific weather conditions resulting in high regional variability in terms of agricultural systems and practices [START_REF] Vintrou | Mapping fragmented agricultural systems in the sudano-sahelian environments of africa using random forest and ensemble metrics of coarse resolution modis imagery[END_REF][START_REF] Lobell | Cropland distributions from temporal unmixing of modis data[END_REF]. The upcoming availability of SENTINEL-2 data opens up new prospects for research, including methodological developments related to agriculture monitoring. By mid-2015, this future Earth Observation System will propose images of i) higher resolution (10-60 m depending on spectral bands) and frequency (10 days in 2015 and 5 days in 2016) allowing a fine agricultural monitoring adapted to the study of crops in areas where agriculture is fragmented, ii) with significant swath (290 km) appropriate for regional and global studies, and iii) with a large number of spectral bands [START_REF] Witten | Data mining: Practical machine learning tools and techniques[END_REF] allowing the characterization of patterns of land use, and quantitative estimation of biophysical variables related to the crop conditions. The pair of Sentinel-2 satellites will thus soon represent the best compromise between spatial and temporal resolution and will replace moderate-resolution images such as MODIS for agricultural monitoring.

To deal with such high spatial resolution images and complex landscape, object-based image analysis is an interesting approach. An overview of the development of object based methods can be found in [START_REF] Blaschke | Object based image analysis for remote sensing[END_REF]. These methods are used in the expectation that it will divide the image into i) relatively homogeneous, and ii) semantically significant groups of pixels. Whereas in classical pixel approaches spatial concepts are not used, in object-based methods a pixel is not studied alone, but together with its neighborhood, and this adds spatial information to the objects [START_REF] Blaschke | What's wrong with pixels? Some recent developments interfacing remote sensing and gis[END_REF]. Dealing with agriculture, the object-based image analysis (OBIA) can help to delineate field boundaries, and thus to reach classification results at field scale. It is thus particularly suitable for high spatial resolution images. However, OBIA requires an expert intervention through supervised methods, which can be difficult when dealing with important volume of data. As the number of sensors of higher spatial and temporal resolutions and possibilities of data sharing are increasing, a generation of new tools is being developed, which is able to handle large volumes of data but also to automatically extract knowledge from databases of multiple sources. Since recently, these data mining tools are beginning to be used in the field of remote sensing [START_REF] Pitarch | Mining sequential patterns from modis time series for cultivated area mapping[END_REF][START_REF] Julea | Efficient spatiotemporal mining of satellite image time series for agricultural monitoring[END_REF]. An example is the prediction of land use from time series of remote sensing images. In this case, data mining patterns' extraction and classification algorithms can be employed to perfectly solve this task and they are able to scale up over big dataset [START_REF] Witten | Data mining: Practical machine learning tools and techniques[END_REF]. In this context, the present study aimed at testing the potential of the future mission SENTINEL-2 to map croplands in a region of Madagascar characterized by small size fields, a large heterogeneity of the cropping practices, and frequent cloud covering. The overall objective of this proposal was to provide new products from the future satellite mission, based on existing (SPOT satellite time series) or recent (PLEIADES) missions to support early warning systems for food security in fragmented agriculture. For this, we developed two different approaches to map a cropland mask in fragmented landscapes: i) a classical remote sensing method using image object-based analysis, expert rules and supervised classification, and ii) an original method based on data mining techniques. This paper deals mainly with the data mining approach as an alternative to conventional methods for defining a learning mechanism based on multi-source data. The object-based Remote-Sensing (RS) and Data Mining (DM) classification results are compared using error matrices based on ground sample points. The same methodology is currently being developed for cropping systems mapping.

STUDY ZONE AND MATERIAL

Study area Study area Study area Study area

Madagascar is an island country in the Indian Ocean, off the coast of Southeast Africa. Our 60*60 km study zone is located near Antsirabe, the capital of the Vakinankaratra region, in the central highlands. This region has the second highest population density of the country and is characterized by terraced, rice-growing valleys lying between grassy hills. Despite its small size (60*60 km), this study area is characterized by heterogeneous landscapes. The irrigation systems are well developed, and use all available water, which flows through narrow canals for considerable distances. Only the areas that cannot be irrigated are planted in dryland crops. Narrow terraces ascending the sides of steep valleys are mainly settled/planted with rainfed maize, cassava, and beans. The main crops such as maize and rice are sown at the beginning of the rainy season (between October and December) and harvested at the end (from March to May). Some of the plots cover no more than a few square meters. The mean size of an agricultural field is very small (about 0.03 ha) but contiguous fields with the same crop type can often result in larger crop patches.

Ground data Ground data Ground data Ground data

Fields surveys were conducted in Madagascar during the growing peak (end of February) of the 2012-2013 cropping season in order to characterize the main cropping systems. A total of 324 GPS waypoints (247 cropped and 90 non-cropped) were registered in the study area, chosen according to their accessibility and to be as well representative of the existing cropping systems as possible. The data gathered during the field survey concerned farmers' practices (type of crop, use of fertilizers and irrigation). GPS waypoints were also registered on different types of natural vegetation to obtain data on the non-crop class. This classical remote-sensing method consisted in classifying SPOT images in three steps: : i) a segmentation of SPOT images in objects, ii) a mask of urban/artificial areas and a classification of the toposequences based on expert rules, and iii) in each toposequence, a crop-non crop supervised classification of the objects based on ground data.

Segmentation

The study area was first segmented so that objects represent plots or groups of plots in the cultivated area, using SPOT images. Considering that field characteristics include a temporal pattern (crop seasonality) and a specific structure (human print), we assumed that the spatio-temporal variability of NDVI and textural indices of SPOT images can be used to segment and classify the study area. We used eCognition software, and for processing time reasons, we chose only two contrasted SPOT images free of clouds in the available time series (one during the vegetation peak on the 3 rd of March, one during the dry season on the 21th of May) to derive these indicators (mean NDVI, mean variance and Euclidian textures). We tested varying combinations of segmentation parameters (shape and compactness) for optimized boundary separation and obtained about 1 300 000 objects. The average object size is about 0.24 ha, which can be considered for the cultivated domain as a "group of fields".

Mask of urban and artificial areas and classification of toposequence

Urban and artificial areas were first isolated thanks to expert rules based on thresholds of brightness, euclidian texture, and NDVI.

In Madagascar, the location of the fields in the toposequence is an important driver of the cropping system as it has a direct impact on the soil quality and water conditions. Basically, irrigated rice is grown in shallows, whereas rainfed rice or maize are found on hills or uplands. To assign a class of toposequence to each field or goup of fields thus helps in reducing the variability of spectral responses of cropping systems used in the following supervised classification step. The toposequence was classified in 4 classes (basins or shallows, lowlands and lower parts of the hills, hills, and uplands) thanks to the use of information extracted from the SPOT DEM processing (slopes, hydrological network) and thresholds (e.g. uplands objects have a slope lower than 3 degrees) or neighborhood rules (e.g. shallows objects intersect with water system, objects belonging to lower parts of the hills touch objects classified as shallows…).

Supervised classification

Inside each class of toposequence, the objects were classified in "crop" or "non crop" using a supervised maximum likelihood classification as proposed in eCognition software. The object-based classification works in the same way as a pixel-based classification with the difference that we do not classify each pixel but combine all pixels of each object and classify them together [START_REF] Walter | Object-based classification of remote sensing data for change detection[END_REF]. In this study, we used the mean value of all pixels of an object in the four SPOT spectral bands and the mean NDVI value of the two selected images, and textural variance calculated on the SPOT NDVI image of March image (maximum of the season). The maximum likelihood classification was conducted thanks to 80% of the ground database and the afore-mentioned attributes associated.

Accuracy calculation

The accuracy of the resulting map, referred hereafter as RS classification, was assessed thanks to a five-fold cross-validation of the classification. A random sample of one fifth of the training set was used for validation purposes. Thereby, for each fold, 20% of the total GPS waypoints were left out, and the supervised classification was recalculated using a new training set consisting of the remaining 80% of the database. The overall accuracies for each fold were recorded and averaged to obtain the overall accuracy of the RS method.

3.2 3.2 3.2 3.2 Data mining Data mining Data mining Data mining (DM) method (DM) method (DM) method (DM) method

A classification model was developed to discriminate between cropped and non cropped area using data mining process. Our proposal involved three main steps: i) satellite-derived metrics were calculated for the 324 plots corresponding to the ground samples, ii) the PrefixSpan data mining algorithm found the frequent sequential patterns of cropped and non-cropped plots, iii) these frequent patterns were used by data mining classification algorithms (Naive Bayes, Random Forest, Decision Tree and Support Vector Machine) and thanks to its attributes, each plot was affected to "crop" or "non-crop" class. These three steps are detailed further.

Attributes extraction

Crops spatial and temporal behaviors can be captured through a set of attributes such as vegetation indices, intra-plot organization and plot layout in the landscape, and vegetation seasonality. These attributes are known to be accessible using time series of multispectral images. Several metrics were thus calculated and associated to each of the 324 plots of the database, whose outlines where digitalized thanks to PLEIADES 50 cm spatial resolution imagery:

-Static information, such as localization in the toposequence, plot size and distance to the river but also SPOT Haralick textural indices describing the plot "organization" and its place in the landscape and calculated at two acquisition dates (March and May). -Temporal information from the entire SPOT time series (reflectance in the four SPOT spectral bands, mean and max NDVI per plot for the 25 images). A linear interpolation of these temporal variables was conducted on the cloudy values.

Extraction of frequent patterns

To establish the link between the crop or non-crop land cover and these various indicators, we used the PrefixSpan algorithm [START_REF] Pei | Mining sequential patterns by pattern-growth: The prefixspan approach[END_REF] to find discriminating sequential patterns of the cropped or non cropped plots using 80% of the dataset. This algorithm extracts all frequent sequential patterns that have a "support" greater than a given threshold. A support of a sequential pattern is the number of objects in which the considered pattern appears.

Classification process

The extracted frequent patterns are used to establish "classifiers" defining if a plot is more likely to be cropped or not according to its static and temporal attributes. For this point, several machine learning algorithms are available in the WEKA tool; more precisely, the following classification techniques were applied on the data set: Naive Bayes, Random Forest, Decision Tree and Support Vector Machine. We choose these data mining models as they span over different assumptions and they well cover different families of classification algorithms: -Naive Bayes [START_REF] Witten | Data mining: Practical machine learning tools and techniques[END_REF] is a probabilistic-based algorithm that employs the "Bayes principle" in order to make its prediction. It assigns a new object to the class that maximizes its likelihood. -Random Forest [START_REF] Breiman | Random forests[END_REF] is an ensemble learning schema that builds a multitude of random decision trees. It makes its prediction on a new example as the mode of the classes predicted by each individual tree. -Decision tree [START_REF] Witten | Data mining: Practical machine learning tools and techniques[END_REF] model the training data using a tree-shape structure. Internal nodes of the tree represent test over description variables while the leaves represent class assignments. A new instance is classified following a root-leaf path induced considering the test in the inner nodes. -Support Vector Machine (SVM) is one of the most effective and recent classification techniques proposed in the machine learning community [START_REF] Cristianini | An introduction to support vector machines and other kernel-based learning methods[END_REF]. This approach searches for a set of support vectors inducing an hyperplane (in the space in which data are represented) able to well separate instances of different classes and obtaining, at the same time, as much generalization as possible. The decision on a test instance is done considering its distance with regards to the support vectors.

Accuracy calculation

These different classification processes were then applied to the 20% of the waypoints left, using a fivefold cross-validation as for the Remote-Sensing method.

RS and DM RS and DM RS and DM RS and DM approaches approaches approaches approaches comparison comparison comparison comparison

The RS and DM classifications obtained after the 5 fold cross validation were evaluated through the error matrices based on the ground data set (324 GPS waypoints). The classification accuracy criteria were: i) the fraction of correctly classified pixels, ii) the commission and omission errors. In addition, for DM classifications, the four DM algorithms were compared through their overall accuracies.

RESULTS

The four data-mining classification algorithms gave good accuracies (from 79 to 84%) but the most accurate classification was derived from the Support Vector Machine (SVM) approach (Table 1).

Algorithm Overall accuracy

NaiveBayes 78%

Random Forest 82%

Decision tree 79% SVM 84%

Table 1. Overall accuracies for the four classification algorithms used in the DM methodology.

The remote sensing and data mining (SVM) approaches showed equivalent overall accuracies (82% vs. 84% for RS and DM methods respectively). Both methods provided stable results for the crop class, that is to say a commission of pixels equivalent to the omission (Table 2). Omission and commission errors were for both methods limited for the crop class (between 7 and 16%), whereas they were quite important for the non-crop class (from 20 to 38%). Figure 2 shows the spatial distribution of cropland in our study area (in this example with the RS approach). As expected, the majority of shallows are cultivated, and rainfed crops are colonizing gradually the hills .

RS_method DM_method

CROP

DISCUSSIONS AND PERSPECTIVES

Two approaches were developed and compared for mapping cropped areas small growers agricultural regions such as in Madagascar. The first method (Remote Sensing or RS) involved an object-based classification, and the second method was a data mining approach (DM). The RS method showed a fraction of pixels correctly classified of 82%, against 84% for the DM approach. The crop class was for both methods better classified than the non-crop class, which is certainly due to the number of crop samples higher than the non-crop ones (247 cropped vs. 90 non-cropped samples).

Misclassifications per class (crop and non-crop) were between 11 and 34% for the RS approach and between 7 and 38% for the DM approach, which can be explained by two main factors:

-cropped patches/objects too small: i) to be detected by SPOT at 10 m resolution, ii) to be separated from the surrounding natural vegetation, iii) to extract a pure signal of the sole cropped field when mean radiometric values are extracted for DM process for example. In this region of Madagascar, the mean plot size is 0.03 ha, which represents less than 2*2 SPOT pixels.

-insufficient reference data collection leading to small size training problem. According to [START_REF] Muñoz-Marí | A support vector domain description approach to supervised classification of remote sensing images[END_REF], training samples should be exhaustive and made up of samples that completely describe the intra-class variability, to encompass all the possible spectral signatures in the classes (cropped and non-cropped domains in our case). However, our study zone is suffering from specific weather conditions resulting in high regional variability in terms of natural landscapes, agricultural systems and practices. Our ground database may not contain samples describing all the land-cover classes present in the investigated area. In both methods, the results could be improved with a bigger training dataset, which would also allow the use of an independent validation dataset for more rigorous statistical results [START_REF] Foody | Thematic map comparison: Evaluating the statistical significance of differences in classification accuracy[END_REF]. About the object-based remotesensing techniques, using more than two SPOT images for the generation of the cropland mask would be one solution to further reduce errors in both segmentation and field-masking. But this makes the RS method even more cumbersome and time-consuming, and the use of a calculation server is recommended. Whereas they obtained similar classification accuracies, these two methods differ widely. Thus, for fair comparison of the classifications it is important to note some specific aspects. First, from a same data set, the RS method used less data than the DM method. The object-based RS method being "user-dependent", we chose indicators and SPOT images acquired at given interest dates that seemed essential to distinguish crop class of non-crop class, so as not to saturate the eCognition software with too many images. That is to say this method used only 2 SPOT images and 2 textural indices, whereas the DM method was based on the whole data set (25 SPOT images and their derived metrics and more than 60 textural images as an example). The extraction of frequent patterns step is the highlight of the DM method. Unlike conventional method with classifiers such as Random Forest [START_REF] Vintrou | Mapping fragmented agricultural systems in the sudano-sahelian environments of africa using random forest and ensemble metrics of coarse resolution modis imagery[END_REF] or SVM, this pretreatment step is used to extract temporal behavior that could not be detected otherwise. The advantages of this DM approach are also its ability to handle quantitative and qualitative data but also dynamic and static data and to do so without a priori, in a timely manner [START_REF] Vintrou | Data mining, a promising tool for largearea cropland mapping[END_REF]. In contrast, the RS method is heavy in its implementation: it mobilizes a full-time expert for the eCognition experts rules to define, and is thus very time consuming. Consequently, as confirmed by [START_REF] Vintrou | Data mining, a promising tool for largearea cropland mapping[END_REF], the data mining procedure is generally recommended, primarily in studies that mobilize wide datasets. Furthermore, to the best of our knowledge, few authors have addressed the problem of classifying multidimensional temporal data [START_REF] Qin | Efficient learning from massive spatial-temporal data through selective support vector propagation[END_REF][START_REF] Tseng | Effective temporal data classification by integrating sequential pattern mining and probabilistic induction[END_REF] and sequential pattern mining of remote sensing images has only been applied at the pixel level without taking into account texture information in the mining process. Many of the problems in mapping land cover noted in the literature relate to the methods used to extract the land cover information from the imagery. This has driven a considerable amount of research into classification methods and supervised classifications in particular [START_REF] Foody | A relative evaluation of multiclass image classification by support vector machines[END_REF]. Seeing that their classification accuracy is generally the same order of magnitude as that obtained with classical classifiers [START_REF] Pitarch | Mining sequential patterns from modis time series for cultivated area mapping[END_REF], researchers are trying to automate methods and to find methods that maximize the information extraction from the dataset without a priori. Support vector machines (SVM) and Random Forest have recently attracted the attention of the remote sensing community [START_REF] Vintrou | Mapping fragmented agricultural systems in the sudano-sahelian environments of africa using random forest and ensemble metrics of coarse resolution modis imagery[END_REF][START_REF] Pasolli | Svm active learning approach for image classification using spatial information[END_REF][START_REF] Maulik | A self-trained ensemble with semisupervised svm: An application to pixel classification of remote sensing imagery[END_REF][START_REF] Du | In Hyperspectral remote sensing image classification based on the integration of support vector machine and random forest[END_REF][START_REF] Gislason | Random forests for land cover classification[END_REF][START_REF] Pal | Random forest classifier for remote sensing classification[END_REF][START_REF] Stumpf | Object-oriented mapping of landslides using random forests[END_REF], as they have considerable potential for the classification of remotely sensed data. The same RS and DM methods are currently being developed for cropping systems mapping. Further analysis will consist in testing the potential of the future mission SENTINEL-2 for crop monitoring and estimation of agricultural production.

CONCLUSION

This study showed the relevance of the use of data mining tools for crop mapping in regions with fragmented agriculture, using decametric images. This should be even clearer in the future, as the new satellites such as Sentinel-2 are expected to generate a large volume of data to store and process. This data mining techniques appear to be robust enough to be applied to a diverse variety of data sets and to be able to integrate information extracted at multiple spatial and temporal scales.

Figure 1 .

 1 Figure 1. Map of the study area around Antsirabe showing the geographic location of the 324 fields sampled on the 2013/03/03 SPOT5 image.

  the growing season extending from October 2012 to May 2013, combined acquisitions of SPOT4 and SPOT5 acquired from SEAS-OI satellite receiving station in Reunion Island or from CNES (Centre National d'Etudes Spatiales) SPOT4Take5 experiment were conducted and allowed us to obtain a time series of 25 decametric images with an average time repeatability of 12 days. These images were corrected geometrically and radiometrically (TOA reflectance). A digital elevation model (SPOT DEM at 20 m spatial resolution) was also acquired in order to extract the location of agricultural fields in the toposequence, thus giving information on the irrigated or rainfed regime of each concerned field. Finally, very high resolution PLEIADES images were acquired at the maximum of the growing season on our study zone to assist in the identification of the fields' outlines of the ground database.

Figure 2 .

 2 Figure 2. Crop classification of the study area around Antsirabe using the object-based remote-sensing method.

Acknowledgments

This work was supported by CNES funds (E. Vintrou's fellowship and V.Lebourgeois' TOSCA project). The authors would like to thank the SEAS-OI reception station in Reunion Island for the SPOT data access, and the JECAM network for integrating the Malagasy site in the initiative.