F Damay

J Sottmann

F Lainé

L Chaix

M Poienar

P Beran

E Elkaim

F Fauth

L Nataf

A Guesdon

A Maignan

C Martin

Magnetic phase diagram for Fe 3-x Mn x BO 5

The heterometallic ludwigite system Fe3-xMnxBO5 recently investigated for its ferroelectric properties has been studied using synchrotron and neutron diffraction, combined with XANES and magnetisation measurements. The results show that the Pbam crystal structure is preserved with little structural distortions up to x = 1.5, and that divalent Mn is substituted preferentially on the 3LL2 sub-lattice unit. As x increases, and up to Fe2MnBO5, the decoupled magnetic sub-lattices character of Fe3BO5 is preserved : magnetic order on 3LL1 (k1 = (0 0 1 2 ), moments along b) survives with reduced magnetic moment, while the correlation length of the magnetic order on 3LL2 (k2 = (0 0 0), moments along a) decreases. In contrast, for x = 1.5, a new k = (0 0 0) magnetic ordering, coupling both sub-lattices, is observed, with all moments aligned along c. These results provide new insight on the physical properties of the system, which are discussed in terms of three main parameters : (i) non-linear evolution of the substitution on each sub-lattice, (ii) changes in the direct-exchange and super-exchange couplings as Mn 2+ (3d 5 , isoelectronic with Fe 3+ ) is introduced in the structure, and (iii) competing easy-axis anisotropy and magnetic exchanges along the 3LL legs in the decoupled sub-lattice regime. These three parameters are at the origin of an extremely rich (x, T) magnetic phase diagram in the Fe3-xMnxBO5 system.

I. INTRODUCTION

Ludwigite oxyborates correspond to the M 2 M'BO 5 formula (where M and M' are transition metals), as a reference to the mineral Mg 2 FeBO 5 [1]. Vonsenite Fe 3 BO 5 [2] is one of the most studied ludwigites [3], [4], [5] ; it crystallizes at room temperature in the Pbam (# 55) space group (a = 9.462 Å, b = 12.308 Å, and c = 3.075 Å), with four non-equivalent iron sites, Fe1 (2a), Fe2 (2d ), Fe3 (4g) and Fe4 (4h) (Figure 1a), following a commonly used labeling [6], [7], [8]. Its structure may be viewed as FeO 6 octahedra sharing edges and corners, to build five octahedra long and three octahedra wide zig-zag walls parallel to the c direction (Figure 1a). These walls delimit triangular tunnels, also running along the c axis, occupied by boron atoms in triangular BO 3 coordination (O1, O3 and O5 in Figure 1a). Another structural description is also used in the literature [9], with two types of three-leg ladder (3LL) sub-lattices, consisting of three edge-or corner-sharing octahedra units, or triads, stacked along c : Fe4-Fe2-Fe4 (3LL1) and Fe3-Fe1-Fe3 (3LL2) (Figures 1b and1c). Fe 3 BO 5 presents interesting physical properties, owing to the mixed valency 2 Fe 2+ : 1 Fe 3+ , and the fact that Fe 3+ species (S = 5/2) occupy 3LL1 sites, while sites 1 and 3 (3LL2) are occupied by Fe 2+ (S = 2) only [4], [10]. Below 290 K, charge ordering (CO) on 3LL1 leads to a supercell with a doubling of the c parameter, as evidenced by single crystal X-ray and electron diffraction [6], [8], [11]. These unusual features also impact magnetic properties, with two magnetic transitions, corresponding to the independent orderings of 3LL1 (T N 1 = 112 K) and 3LL2 (T N 2 = 70 K) [8]. Fe 3 BO 5 was also recently shown to exhibit magnetodielectric and multiferroic properties [11], and was also explored as a potential anode for lithium-ion batteries [12]. A number of interesting features can therefore be found in ludwigites : low-dimensional magnetic units, coexistence of paramagnetism and magnetic order, or mixed valency with a non-random distribution of the species on different crystallographic sites. Although the ludwigite structure is able to incorporate various elements, including tetravalent cations, as shown by the long list of known minerals exhibiting this structure (e.g. fredrikssonite [13], bonaccordite [14], azoproite [15], chestermanite [16], etc.), few reports deal with homometallic [17] or heterometallic ludwigites containing Mn, the latter focusing mostly on Cu 2 MnBO 5 [18], [19], [20], or Mn 3-x Ni x BO 5 [21], [22]. In the only published study of the heterometallic ludwig-ite system Fe 3-x Mn x BO 5 , Maignan et al. report very distinct dc susceptibilities for the x = 0 and x = 1 members, in addition to superparamagnetic-like spin dynamics for x = 1, in spite of the close spin configurations of Mn 2+ and Fe 3+ , both being d 5 cations [11]. Moreover, the pyroelectric current measurements performed on these compounds reveal a larger polarization value at 5 K for Fe 2 MnBO 5 than for Fe 3 BO 5 , coupled with the disappearance of CO features, urging for a better understanding of the general impact of Mn substitution on the vonsenite properties, also supported by the known importance of CO and Fe octahedral geometry in explaining the physical properties of Fe 3 BO 5 [23]. To this end, an investigation of the Fe 3-x Mn x BO 5 system was undertaken. Synchrotron X-ray and neutron diffraction experiments, combined with magnetic susceptibility vs. temperature and X-ray absorption spectroscopy measurements were carried out. A complex magnetic phase diagram emerges, underlining the role of preferred substitution and its impact on the magnetic exchanges and anisotropy, and sublattices coupling. The quality of the samples was checked by X-ray powder diffraction (XRPD) at room temperature (RT), using a PANalytical diffractometer (using Co or Cu Kα radiations). Small amounts of impurities are difficult to avoid in this system, mainly Fe 3 O 4 and Mn 3 B 2 O 6 for smaller and larger x values, respectively. The samples were of poorer quality for 2 ≤ x ≤ 3, and their analysis was limited to XRPD measurements only. Direct current (dc) magnetic susceptibility (χ) was derived from magnetization data recorded in a field of 100 Oe, on warming from 5 to 300 K after a zero-field (zfc) or field (fc) cooling (MPMS, Quantum Design). Alternating current (ac) susceptibility was measured in the frequency range 10 1 -10 4 Hz (h dc = 0 Oe and h ac = 10 Oe) (PPMS, Quantum Design). X-ray absorption near edge structure (XANES) measurements were performed on the ODE beamline at the SOLEIL synchrotron for the 0.25 ≤ x ≤ 1.5 compositions. The X-ray absorption spectra were measured in a transmission configuration and recorded at RT with an energy resolution of 0.5 eV. The spectra were calibrated in energy using Fe and Mn foil references, and normalized using the Larch package [24]. Samples with x = 0.75, 1 and 1.5 were characterized by synchrotron X-ray powder diffraction (SXRPD) on the CRISTAL beamline at the SOLEIL synchrotron (λ = 0.6694 Å) at RT and on BL04-MSPD at the ALBA synchrotron (λ = 0.4421 Å) in the 80 K to 300 K range. The powders were 20 µm sieved and filled in borosilicate capillaries (Ø 0.5 mm). Neutron powder diffraction (NPD) vs. temperature was performed on the G4.1 diffractometer (λ = 2.426 Å) from 1.5 to 300 K, at LLB-Orphée, for x = 0.75, 1 and 1.5, and on the Meredit diffractometer (λ = 1.4618 Å), at the Nuclear Physics Institute, in the same temperature range, for x = 0.5, 0.75, 1 and 1.5. Rietveld refinements were performed with the Fullprof program [25]. Symmetry analysis was carried out using the FullprofSuite software [25] and the Bilbao Crystallographic Server [26], [27].

II. EXPERIMENTAL

III. RESULTS

A. Crystal structure study of Fe3-xMnxBO5 1. Evolution of the crystal structure of Fe3-xMnxBO5 with

x at room temperature a. Cell parameters All samples within the series exhibit the ludwigite crystal structure with Pbam space group. This agrees with the electron diffraction study performed at RT for x = 0 and 1, which confirmed the Pbam cell with no superstructure [11]. The evolution of the lattice parameters, obtained from Rietveld refinements of the XRPD data for 0 ≤ x ≤ 3, is shown in Figure 2. For x = 0, the obtained cell parameters are in good agreement with those previously reported [4]. This is, however, not the case for Mn 3 BO 5 (x = 3), for which the published single-crystal data [17] reports smaller cell parameters than for Fe 3 BO 5 , in contrast with our observation of a volume increase of ≈ 5% from x = 0 to 3. As shown in Figure 2, the cell volume increases with x from x = 0 to 2, and then remains roughly constant. The lattice parameters all increase accordingly with x from x = 0 to 2, above which (x > 2), c becomes nearly constant, while b increases and a decreases. Comparing ionic radii (IR) of di-and tri-valent iron and manganese (IR are given in the inset of Figure 2 [28]), this behavior suggests that manganese is divalent up to x = 2. For x > 2, Mn 3+ (with similar size to Fe 3+ ) may be present, and could be at the origin of the plateau observed in the evolution of the cell volume as a function of x. This will be further confirmed in the light of the cationic distribution and species on each ladder, in section III A 1 d.

b. Cationic distribution The analysis of the RT NPD data for x = 0.5, 0.75, 1 and 1.5 allows one to quantify the Fe and Mn distribution on the four cationic sites of the ludwigite structure, owing to the significant difference in the Fe/Mn neutron scattering lengths (0.954 and -0.373 10 -12 cm, respectively). From the comparison of the refinements performed on different neutron diffraction datasets for a given sample, the site occupancy is estimated to be known with a precision of the order of 5% for the four sites (see Table I). The Fe/Mn ratios determined from the refinements are in good agreement with the nominal compositions. The results are summarized in Figure 3, which represents the evolution of the Mn occupancy (in %) on each site vs. the overall Mn composition. The occupancies of sites 1 and 3 (3LL2) are roughly equal (red full squares and empty circles, respectively), an observation that holds for sites 2 and 4 (3LL1) as well (blue full squares and empty circles, FIG. 2. : Variation (in %) of the lattice parameters a (white stars), b (grey circles), c (black triangles) and cell volume V (black squares) with x in the Fe3-xMnxBO5 series (from Rietveld refinements of XRPD data at RT). Cationic sizes of high-spin Fe 2+/3+ and Mn 2+/3+ in octahedral environments are given in the inset [28]. Lines are guide to the eye. respectively), which means that cationic distribution is nearly homogeneous within each ladder. In contrast, the Mn content in 3LL2 is systematically larger than that in 3LL1. Thus the 3LL2 ladder, which is the one containing only Fe 2+ for x = 0, is preferentially affected by the Mn substitution, but only to some degree, as Mn also substitutes partially 3LL1 before all 3LL2 sites are filled with Mn. This preferred substitution also implies that the 1Fe : 1Mn threshold occurs for different x values depending on the ladder which is considered : x = 0.9 for 3LL2, and x = 2.1 for 3LL1 (black arrows on Figure 3). Another consequence of the Fe/Mn distribution on the transition metal sites is the presence of diffuse scattering of non-magnetic origin (also called Laue monotonic scattering [START_REF] Warren | X ray diffraction[END_REF]), centered on Q = 1.15 Å-1 on all neutron diffraction patterns, from x = 0.75 to 1.5 (inset of Figure 5b, shown for x = 1).

c. Fe and Mn valences Mn K-edge XANES spectra are presented in Figure 4a, along with two reference spectra, MnO (Mn 2+ species) and Mn 2 O 3 (Mn 3+ species). Similar absorption profiles are observed for all the samples, independently of x, with the white line centred around 6550 eV (lower panel of Figure 4a), likewise to the MnO reference (see upper panel of Figure 4a). Thus, the Mn valence in the Fe 3-x Mn x BO 5 series, up to x = 1.5 (highest x value investigated by XANES in this work), is confirmed to be 2+. The amount of Fe 2+ species decreases with increasing x (Figure 4b), confirming the gradual replacement of Fe 2+ by Mn 2+ , which was found to occur preferentially on the 3LL2 ladders (section III A 1 b). Indeed, the comparison with the Fe K-edge XANES reference spectra of FeO (Fe 2+ species) and Fe 2 O 3 (Fe 3+ species) shows that FIG. 3. (color online) : Evolution of the Mn distribution on 3LL1 (sites 2 and 4 drawn as full blue square and empty blue circles) and 3LL2 (sites 1 and 3 drawn as full red square and red blue circles) with x. The green line represents the case of a random distribution of Fe/Mn over both 3LL1 and 3LL2, which thereby become equivalent. The orange dashed line shows the extreme case where Mn is substituted on 3LL2 only, up to an overall composition of 50% of Mn (corresponding to x = 1.5), before gradually substituting 3LL1. The black circles on the horizontal 50% Mn occupancy line correspond to compositions (given by the small arrows) for which the Mn:Fe ratio is 1 in the chosen ladder. Inset : ab projection of the ludwigite structure emphasizing the preferred substitution of Mn on the dark grey octahedral sites 1 and 3 of 3LL2.

for x = 0, the absorption edge is close to that of FeO, in good agreement with the expected 2Fe 2+ :1Fe 3+ ratio. Upon Mn-substitution, the Fe absorption edge shifts to higher energies and smoothly meets the Fe 2 O 3 absorption edge position at x = 1.5.

d. Evolution of interatomic distances and angles

The evolution of the interatomic distances in Fe 3-x Mn x BO 5 was obtained from combined Rietveld refinements using NPD and SXRPD data for x = 1 and 1.5 (Figure 5) and from the literature for x = 0 [8]. The results are summarized in Tables I andII. In Fe 3 BO 5 , the average <FeO> distance depends on the ladder which is considered : the Fe2O 6 and Fe4O 6 octahedra forming 3LL1 are the smallest (with <FeO> = 2.09 Å and 2.06 Å, respectively), while iron octahedra in 3LL2 (Fe1O 6 and Fe3O 6 ) are bigger (<FeO> = 2.15 Å), in agreement with preferred occupation of Fe 2+ on 3LL2. A similar observation can be made when increasing x up to x = 1.5, with a slight increase of the <(Fe/Mn)O> distances in all the octahedra, in agreement with the fact that Mn is only present as Mn 2+ (see sections III A 1 a and III A 1 c). With regards to octahedral distortion, in Fe 3 BO 5 , Fe1O 6 and Fe2O 6 (which are in the middle of the triads forming 3LL2 and 3LL1, respectively) are compressed, with one short apical Fe-O distance (x 2) of 2.04 Å and 2.06 Å, respectively, and one (x 4) long distance in the basal plane, of 2.20 Å and 2.11 Å, respectively. The Fe3O 6 and Fe4O 6 octahedra are more distorted, with three sets of Fe-O distances, ranging between 1.95 Å and 2.21 Å. In all octahedra, the O-Fe-O angles also clearly deviate from 90 • .

Comparison with Fe 1.5 Mn 1.5 BO 5 shows that, although the (Fe/Mn)2O 6 octahedron of 3LL1 is more regular than in Fe 3 BO 5 , there is actually little evolution of octahedral distortions with x (Table II). This particular behavior probably originates from the fact that there is no possible atomic displacement along the c-axis (all atoms being on (x y 0) or (x y 1 2 ) sites), and that the transition metal octahedra are more flexible than the BO 3 units with their short B-O distances (≈ 1.4 Å). This underlying rigidity of the BO 3 triangles could also be the reason why high levels of Mn substitution (x ≥ 2) seem difficult to achieve in the series. It should be underlined further that O4 has a systematically "underbonded" character (short (Fe/Mn)3-O4 and (Fe/Mn)4-O4 distances), which is likely correlated with its specific position, linking both types of ladders and two zig-zag walls, while not being involved in a BO 3 triangle. It leads to a clear displacement of atoms on sites 3 and 4 of the ludwigite structure from the center of their O 6 octahedra.

Crystal structure of the Fe3-xMnxBO5 series at low temperature

For x = 0.5, 0.75, 1 and 1.5, the Pbam crystal structure is observed down to 4 K from high resolution NPD, and further confirmed by SXRPD data at 122 K for x = 1. The lack of charge-ordering (CO) superstructures reported earlier by electron microscopy for x = 1 down to 90 K [11] supports the fact that Mn substitution suppresses charge ordering at least for x ≥ 1, but this remains to be confirmed for x = 0.5 and 0.75. For all samples up to x = 1.5, the contraction of the cell parameters with temperature is regular within the experimental error, and similar along a, b, and c. Table III summarizes the results of NPD data Rietveld refinements performed at 180 K and 4 K for x = 1. It shows that there is a general decrease, with decreasing temperature, of the distances between transition metal sites, with the exception of the distance between sites 1 and 3 (d 1-3 ) in 3LL2, and sites 1 and 4 (d 1-4 ), which slightly increases or stays constant within the standard deviation. Similarly, the contraction of the (Fe/Mn) octahedra is only slight, and the octahedral distortion remains almost constant when temperature decreases.

TABLE I: Results of combined SXRPD and NPD Rietveld refinements of Fe2MnBO5 and Fe1.5Mn1.5BO5 at 300 K (space group Pbam, # 55). (Fe/Mn)1 and (Fe/Mn)2 are on Wyckoff sites 2a (0 0 0) and 2d ( 12 0 1 2 ) respectively. All other atoms are on sites 4g (x y 0) or 4h (x y 1 2 ). Cell parameters and atomic positions in Fe3BO5 (x = 0) at 320 K (from single-crystal X-ray diffraction data [8]) are given for comparison. Isotropic thermal displacements parameters B were constrained to be identical for a given element. The B values obtained from SXRPD data are (in Å2 ) : B F e/M n = 0.4(1), BB = 0.3(1); BO = 0.3(1) for x = 1, and B F e/M n = 0.7(1), BB = 0.2(1); BO = 0.8(1) for x = 1.5.

Composition

x = 0 [8] x = 1 x = 1.5 Mn for Fe substitution has a strong impact on the magnetic properties of the system. Qualitatively, two types of behaviors are observed depending on x, which are described below. For all compounds, the inverse of the susceptibility curve does not reach a linear regime up to 300 K, which indicates magnetic interactions at high temperature.

1. Magnetic properties and magnetic orderings for x ≤ 1.0

The T N 1 and T N 2 values used in the following are derived from susceptibility measurements (Figure 6) and are also listed in Table IV for four selected compositions. The χ(T) curve of Fe 3 BO 5 (x = 0, Figure 6a) shows two magnetic transitions, at T N 1 ≈ 112 K and T N 2 ≈ 70 K, with a strong zfc/fc effect for T < 70 K, which extends up to T N 1 . All those features are in good agreement with those published earlier [10], in which T N 1 and T N 2 values of 114 K and 74 K, respectively, were reported. These two magnetic transitions correspond perfectly to the independent orderings of the 3LL1 (below 112 K) and 3LL2 (below 70 K) ladders described in [8]. For x = 0.25 and x = 0.5 (Figure 6b and6c), both transitions are still present, but the kink characterizing T N 1 is hardly visible (Figure 6f), while the hysteresis below T N 2 persists. T N 1 and T N 2 values are seemingly not affected by Mn substitution in this range of x. The main difference with x = 0 is the fact that the 5 K value of the fc susceptibility is negative, with the fc susceptibility curve crossing the zfc one below a crossing point temperature T cross . This is a well-known feature of magnetic compounds with two magnetic sub-lattices [START_REF] Smart | [END_REF] and confirms the fact that small levels of Mn substitution preserve the distinct orderings of 3LL1 and 3LL2 units, a rare observation in heterometallic ludwigites, to the best of our knowledge. For higher x (e.g. x = 0.75, Figure 6d), the peak shape of the fc χ(T) below T N 2 disappears, while the difference between zfc and fc curves persists. A small kink at T N 1 is still observed. T N 1 and T N 2 are reduced with respect to 0 ≤ x ≤ 0.5 : for x = 0.75, T N 1 ≈ 100 K and T N 2 ≈ 55 K. Increasing the Mn content further, a drop of the susceptibility maximum, by a factor 10 compared to x = 0, is observed (x = 1, Figure 6e). Two magnetic transitions are still identified, but at lower temperatures with respect to smaller x values (see Table IV). The difference between zfc and fc curves is also present, like for smaller x values, but starts between T N 1 and T N 2 .

TABLE II: Selected atomic distances (in Å) at 300 K (with multiplicity) in Fe2MnBO5 and Fe1.5Mn1.5BO5 at 300 K. For simplicity, the distance between (Fe/Mn) sites is written using only the site number, e.g. the distance between (Fe/Mn)1 and (Fe/Mn)3 is noted d1-3. Atomic distances in Fe3BO5 (x = 0) at 320 K (calculated from [8]) are given for comparison purposes.

Composition

x = 0 x = 1 x = 1.5 (Fe/Mn) To go further in the understanding of these complex magnetic behaviors, neutron diffraction vs. temperature was performed for x = 0.75 and x = 1. Similar behaviors are observed for both compounds. Below T N 1 , additional peaks appear on the NPD patterns (x = 1, Figure 7), which can be indexed by the commensurate propagation vector k 1 = (0 0 1 2 ), as in the model proposed for Fe 3 BO 5 [8]. Rietveld refinements supported by symmetry analysis (Table V) indicate that only the 3LL1 sub-lattice orders below T N 1 . As there is no evidence of a structural transition in Mn substituted samples, a simple Pbam cell was considered for the symmetry analysis. Magnetic ordering of symmetry nonequivalent sites 2 and 4 (which form 3LL1) follows the irreducible representation (irrep) Γ6, with two basis vectors ψ1 = (1 0 0) and ψ2 = (0 1 0). Interestingly, for the Γ6 irrep, magnetic ordering is also allowed on sites 1 and 3 (3LL2), but only with moments parallel to c, which is not compatible with the observed magnetic intensities. The best refinement results therefore correspond to a magnetic ordering, below T N 1 , on the 3LL1 sub-lattice only, and can be described as FM ladder rungs, arranged AFM along c, with spins parallel to b (Figure 7b). The magnetic space group is then P b nma (BNS #62.451) in a cell doubled along c. This group is not compatible with ferroelectricity or any magnetoelectric effect [26]. The moments on site 2 and site 4 are not equivalent symmetry-wise and can be refined independently : for x = 1 at 2 K, values of 3 µ B and 2.2 µ B are obtained on site 2 and 4, respectively (Table IV and Figure 7e). This is only slightly lower than the values reported for Fe 3 BO 5 [8] (3.9 µ B and 2.7 µ B at 10 K, respectively, which were already distinctively smaller than the 5 µ B and 4 µ B expected for spin-only values of Fe 3+ and Fe 2+ ), but the tendency to have a larger moment on site 2 (which has the least distorted octahedral environment) than on site 4 is confirmed for both x = 0.75 and x = 1 (Table IV). These moments values, close to those observed for x = 0, are also in good agreement with the fact that 3LL1 is little impacted by Mn substitution up to x = 1 (Figure 3). Below T N 2 , the ordering of the second sub-lattice leads to additional magnetic intensity (x = 1, Figures 7a and7d) on existing Bragg peaks (k 2 = (0 0 0)), likewise to Fe 3 BO 5 [8]. For x = 0.75, the corresponding magnetic Bragg peaks are only slightly broader than the crystal ones (whose width is limited by instrumental resolution), whereas for x = 1, broad magnetic scattering is observed, as highlighted on the inset of Figure 7a for the (0 2 0) Bragg peak. Rietveld refinements, performed using symmetry analysis, indicate that the magnetic ordering of this 3LL2 sub-lattice follows irrep Γ5, that is, AFM configuration within the rungs, with a FM arrangement along c (Figure 7c). Moments are aligned along a, therefore inferring a magnetic anisotropy on 3LL2, like on 3LL1, of the easy-axis type, but orthogonal to the latter. For x = 0.75 at 2 K, the ordered moment values on sites 1 and 3 are 2.9 µ B and 2.8 µ B , respectively. For x = 1, the ordering is only short-range, with a magnetic correlation length estimated about 120 Å, and the maximal ordered moment remains low, around 1.6 µ B (Figure 7e). This value was constrained to be equal for both sites 1 and 3, since the refinement did not allow for a meaningful distinction between the two. This short-range magnetic ordering is in good agreement with the preferred substitu- tion of Mn 2+ on 3LL2, which leads to a Fe:Mn ratio close to 1 on 3LL2 for x = 1. At 2 K, the magnetic space group of the cell is therefore lowered to Pb'am' (BNS #55.358), whose point group is not compatible with ferroelectric or magnetoelectric effects, although the Mn for Fe substitution could actually lower the symmetry locally. Two representations are thus mixed below T N 2 (Γ6 ⊕ Γ5), which means that the magnetic phase transition at T N 2 is first-order, while the transition at T N 1 is second-order. This should also apply to Fe 3 BO 5 , and is in good agreement with specific heat data [31].

For both x = 0.75 and x = 1, signatures of magnetic disorder are also seen on the ac susceptibility curves (Figure 8), which becomes frequency dependent below 30 K for both compositions. As a final remark, in contrast to what was reported for Fe 3 BO 5 [8], the ordering of 3LL2 does not seem to influence the 3LL1 ordered moment value.

2. Magnetic properties and magnetic ordering for 1.0 ≤ x < 2.0

For larger x values (1 < x < 2) the χ(T) curves still display two transitions, as shown in Figure 9a for x = 1.5, corresponding to the splitting of the zfc and fc curves at T N ≈ 100 K, and to the downturn of the zfc curves at T down ≈ 30 K. Neutron diffraction performed on Fe 1.5 Mn 1.5 BO 5 shows a unique transition at T N = 100 K, corresponding to the appearance of magnetic intensity, with the propagation vector k = (0 0 0). Rietveld refinements (Figure 10) based on symmetry analysis indicate that the magnetic order follows one single representation, Γ1, for the four different sites. This imposes moments along c, and the magnetic space group is therefore Pbam (BNS #55.353, not compatible with ferroelectric or direct magnetoelectric effects). For sites 1 and 2, this couples the components of (x, y, z) and (-x+ 1 2 , y+ 1 2 , -z) AFM along c. For sites 3 and 4, the coupling within (x, y, z) and (-x, -y, z), as well as (-x+ 1 2 , y+ 1 2 , -z) and (x+ 1 2 , -y+ 1 2 , -z) pairs is FM, and the pairs are coupled together antiferromagnetically (Figure 10a). The comparison of Figure 7c and 10a (also summarized in Figure 11) shows how most couplings have been reversed, especially within the triads of former 3LL subunits. There is no symmetry constraint between the moment values on each sites and the refinement is improved significantly by refining them independently. While the moments on sites 2 and 4 are almost identical, 2.7 µ B , there is a significantly lower magnetic moment on site 1 (1.7 µ B ), with respect to site 3 (2.5 µ B ), despite similar Fe/Mn ratios (Table IV). In addition, the magnetic peaks are resolution limited, in contrast to x = 0.75 and x = 1, but a frequency dependence of the ac susceptibility curves (inset of Figure 9a) is still observed around 30 K, like for x = 0.75 and x = 1. It does not seem to be linked with any feature on the NPD patterns, except for a slight decrease of the observed ordered moment on all sites (Figure 9b), which coincides with the decrease in the zfc magnetization curve (Figure 9a) below 30 K.

Fe3-xMnxBO5 magnetic phase diagram

From the susceptibility curves, such as those shown in Figures 6 and9, a (x, T) magnetic phase diagram was built, and is displayed in Figure 11. T N 1 (blue squares) and T N 2 (red squares), corresponding to the ordering of 3LL1 and 3LL2, respectively, are plotted up to x = 1. T N 2 corresponds to the maximum of the peak of the zfc susceptibility curve up to x = 1, which is also in agreement with the T N 2 determined from NPD data. For x > 1, T N is defined as the temperature where zfc and fc χ curves split markedly. In the phase diagram are also reported T cross (crossing point temperature of the zfc and fc curves, white up triangles) and T down , which corresponds for x > 1 to the temperature of the maximum on the zfc susceptibility curve (white down triangles). The temperature at which ac frequency effects are observed TABLE IV. Evolution of TN with x (from susceptibility measurements and [8] for x = 0), and of the ordered moment on each transition metal site (from Rietveld refinement of NPD data) in the Fe3-xMnxBO5 series. The ordered moments for x = 0 were measured at 10 K and are taken from reference [8], while the values for the other compositions were obtained at 2 K. on susceptibility curves is also shown in Figure 11 (white stars).

The main feature of the phase diagram is the existence of two main types of magnetic orders, with a boundary between x = 1 and x = 1.5, characterized by the existence of either two independent magnetic sub-lattices (x ≤ 1) or by a single magnetic network (1 < x ≤ 1.75). Up to x = 0.5, there is little change with x of the magnetic ordering temperatures, which remain roughly constant ≈ 110 K and 70 K, before a sharp decrease is observed for x ≥ 0.75. A decrease of the ordered magnetic moment (Table IV) and the appearance of frequency effects on the ac susceptibility below 30 K are also observed for x ≥ 0.75, likely owing to magnetic disorder. Based on this phase diagram, x ≈ 1.25 should correspond to the absence of ordering on 3LL2, while T N 1 should be reduced to ≈ 70 K. Further increasing x (x ≥ 1.5), one reaches the single magnetic lattice regime, with T N increasing from 100 K, for x = 1.5, up to 115 K for x = 1.75. Low temperature ac susceptibility frequency effects are still observed up x = 1.5, but could be expected to decrease with increasing Mn content, as T N increases and magnetic disorder vanishes. This experimental study proves the originality of the magnetic properties of the Fe 3-x Mn x BO 5 ludwigite borates, coming from an unusual crystal structure, with the addition of preferred Fe/Mn distribution. The different properties which can be impacted when varying x in Fe 3-x Mn x BO 5 are now discussed in more details below.

IV. DISCUSSION a. Charge ordering From [11], it is known that there is no CO in Fe 2 MnBO 5 , in contrast with Fe 3 BO 5 , a result that can be linked with previous reports on other CO systems [32], in which even minute amounts of substitution destroy any ordering of the charges. In Fe 3 BO 5 , the schematic picture of charge ordering concerns 3LL1 only : the extra electron on each triad of 3LL1 (which contains 2Fe 3+ for 1Fe 2+ ) is delocalised at high temperature, and then localizes onto a Fe-Fe pair, to form a dimer. The ordering of the dimers along the ladder is zig-zag like, probably as a mean to minimize structural distortions [8]. In Fe 3-x Mn x BO 5 , because of the preferred substitution of Mn 2+ on 3LL2, CO could have been expected to withstand sizeable levels of substitutions ; 10% of Mn on 3LL1, as evaluated in Fe 2 MnBO 5 , is high enough to destroy CO features at least down to 90 K, however. Interestingly, in spite of the absence of CO on 3LL1, the 3LL1 triad remains ferromagnetic up to x = 1, showing TABLE V. Basis functions for axial vectors associated with irreducible representation Γ6 for Wyckoff site 2d (site 2) and 4h (site 4) of the Pbam space group, with the propagation vector k1 = (0 0 0.5).

Γ6

(x y z) (-

x+ 1 2 y+ 1 2 -z+1) (x y z) (-x+1 -y+1 z) (-x+ 3 2 y+ 1 2 -z+1) (x-1 2 -y+ 1 2 -z+1) ψ1
1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 ψ2 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 that CO dimers do not control the magnetic structure, as it had been suggested in [33], and that their existence has probably less impact on the magnetic ordering than the presence of Fe 3+ on 3LL1 only. This promises to be a very interesting theoretical issue to investigate. In a similar fashion, based on the importance of octahedral distortions in vonsenite [23], [34], [START_REF] Whangbo | Continentino[END_REF], the origin of the preferred substitution, as well as the impact of Mn 2+ on the magnetism of the 3LL2 units, would also be key points to study theoretically.

b. Understanding magnetic exchanges A preliminary step is to check whether the changes induced by Mn 2+ can be explained by the Goodenough-Kanamori rules [START_REF] Goodenough | Magnetism and the Chemical Bond[END_REF] going from x = 0 to x = 1.5. In Fe 3 BO 5 , the FM triad (of edge-sharing octahedra) in 3LL1 is simply explained by a d 5 -d 6 ferromagnetic direct-exchange (with short Fe2-Fe4 distances ≈ 2.78 Å), J 1 (Figure 1c). Along c, FeO 6 octahedra are also linked by edges but the Fe-Fe distance is larger (≈ 3.08 Å), thus close to the limit for a direct-exchange mediated J C . With a Fe-O-Fe angle of about 94 • , a weak d 5 -d 6 super-exchange J C would actually support the observed AF configuration. The coupling between 3LL1 units is mediated by more complex paths, involving super-super exchange, possibly through BO 3 units, which cannot be decided unequivocally at that stage, considering the crystal structure. Within 3LL2 units, as d 6 -d 6 interactions only are present, the strongest interactions should correspond to AFM super-exchange J 2 within the triad (octahedra sharing corner), and to ferromagnetic direct-exchange along c, corresponding to J' C (Figure 1c). The Fe-Fe distance along c is the same as 3LL1 (≈ 3.08 Å), but the Fe-O-Fe angle is actually less distorted, > 90 • in 3LL1 for < 90 • in 3LL2, which explains why d 5 -d 6 interactions are of different signs depending on the ladder, and hence the distinction between J C and J' C . The coupling between 3LL1 and 3LL2 units has a triangular topology. The corresponding exchange path J f (Figure 1c) is through larger Fe-Fe distances (≈ 3.17 Å) between edge-sharing octahedra, and presumably leads to a weaker super-exchange interaction than within a sub-lattice unit. In the Fe 3-x Mn x BO 5 system, it is necessary to consider Mn 2+ , isoelectronic to Fe 3+ (d 5 ) in addition to Fe 3+ and Fe 2+ . Adding Mn 2+ to 3LL2 should lead to similar characteristics to those of 3LL1 along c in Fe 3 BO 5 , that is, antiferromagnetic J' C . The exchange along c in 3LL1 and 3LL2 is ferromagnetic, however, as exemplified in x = 1.5. The fact that, in x = 1.5, FM J C and FM J' C is observed, rather supports the idea that, in the decoupled sub-lattice regime, antiferromagnetic J C in 3LL1 is weak, and likely lies at the threshold between AFM super-exchange and FM (d 5 -d 6 ) direct-exchange.

c. Magnetic sub-lattices coupling

The coupling of both ladders for x = 1.5 is concomitant with the observation of ferromagnetic J C and J' C exchange along c for both 3LLs. Arguably, it can be proposed that, for x ≤ 1, the antiferromagnetic ordering along c, of the 3LL1 spins at T N 1 , prevents the ordering of 3LL2, as the triangular pathways coupling the ladders through J f frustrate the J' C magnetic exchange (whether FM or AFM) [5]. Assuming a strong easy-axis magnetic anisotropy of Fe 2+ [37] [38], the 3LL2 spins cannot order into a non-collinear structure (such as the 120 • magnetic ground state observed in frustrated compounds with triangular ladder topology [39], [40]), and remain idle down to T N 2 . 3LL2 spins eventually order at T N 2 << T N 1 , perpendicularly to the 3LL1 spins : the release of the frustration is here performed through a magnetic decoupling of both lattices. Although unusual, idle spin behavior linked with topological frustration has been reported in other mixed valence systems, like Fe 2+ Fe 3+ 2 F 8 (H 2 O) 2 [41], [42]. This coexistence of three-dimensional (3D) order and frustration remains the main feature of the magnetic ordering of the system Fe 3-x Mn x BO 5 up to x = 1. Other examples of ladders' coupling in the ludwigite system are scarce or difficult to assess, as there are very few published neutron diffraction studies, which mostly concentrate on Fe 3 BO 5 ([8], [5]), and the interpretation of magnetization data is not straightforward, as exemplified by this study. From a literature survey, decoupled ladders could be expected in Co 2 FeBO 5 , or Ni 2 FeBO 5 [43], [44], whereas coupled ladders would be likely in Co 3 BO 5 [45] and Co 2.5 Sn 0.5 BO 5 [46], but this would have to be confirmed by appropriate experiments.

d. Magnetic disorder

The ludwigite system also offers a very interesting approach to study magnetic disorder : preferred substitution can be seen as an additional degree of freedom to adjust the composition of each ladder, concentrating disorder effects on one sub-lattice at a time. Up to x = 1.5, which represents 50% Mn in the system, 3LL1 remains ordered, with a T N varying between 112 K (x = 0) and 85 K (x = 1), increasing again to 100 K for x = 1.5. For x ≤ 1, the ordering of 3LL1 occurs through superexchange pathways that are not sensitive to the magnetic state of 3LL2 (i.e., disordered or ordered), and it could be possible by adjusting x to achieve complete disorder on 3LL2, while preserving order on 3LL1, with potentially interesting applications, such as magnetocaloric effects. A more detailed investigation of the composition range 1 < x < 1.5, which lies at the threshold between two distinct magnetic ground states, will also be an interesting perspective, with unusual effects being expected, such as non collinear magnetic ordering resulting from competing anisotropies or exchange disorder. In this context, substitution of 4+ species should also be of interest, since 4+ species might preferentially substitute on 3LL1 rather than on 3LL2, and arguably prevent magnetic ordering altogether, a scenario that can be proposed to explain the spin-glass state of Co 2.5 Ti 0.5 BO 5 [47]. An inelastic neutron scattering study of the Fe 3-x Mn x BO 5 system is now required to provide a better picture of the dominant magnetic exchange paths in the ludwigite structure, in particular to confirm the different hypothesis about the impact of Mn substitution on magnetic exchanges, magnetic anisotropy and on the sub-lattice coupling.

V. CONCLUSION

This detailed study of the crystal and magnetic structures, and magnetic properties of the heterometallic ludwigite system Fe 3-x Mn x BO 5 , has established a rich phase diagram, originating from its complex network of two crystallographically distinct three-leg ladders. The composition (x) controls both the (Fe/Mn)O 6 octahedral distortions and orbital filling. For small x values (x ≤ 1), the ladders are decoupled and order independently. A reversal of the magnetic exchange signs inside the different triads is observed above a threshold of x ≈ 1.25. In parallel, magnetic exchange along all ladders' legs becomes ferromagnetic, which removes the frustration at the origin of the decoupling of the ladders and leads to a single magnetic transition. Magnetic anisotropy also changes from easy-axis along a or b for x < 1.25, to easy-axis along c for x ≥ 1.5. Magnetic relaxation phenomena below 30 K and reduced ordered magnetic moments on the transition metal sites both attest to magnetic disorder, for 0.75 ≤ x ≤ 1.5. The ability to substitute Mn preferentially on only one of the two ladders is an original way to control both magnetic disorder and ladders' magnetic coupling in this system.

Fe 3 -

 3 x Mn x BO 5 (0 ≤ x ≤ 3) samples were prepared by solid state reaction at high temperature. Amounts of precursors were calculated to respect the O 5 stoichiometry. Mixtures of (Fe, Fe 2 O 3 , MnO and B 2 O 3 ) or (Fe 2 O 3 , MnO 2 , MnO and B 2 O 3 ) were used for 0 ≤ x ≤ 1.75 and 2 ≤ x ≤ 3, respectively. Powders were pressed in the shape of bars or pellets and heated in evacuated quartz ampoules during 48 hrs at 950 • C or 1000 • C, respectively. For neutron diffraction experiments, specific samples (x = 0.5, 0.75, 1 and 1.5) were made from 11 B enriched B 2 O 3 .

FIG. 1 .

 1 FIG. 1. (color online) : (a) Representation of the vonsenite Fe3BO5 structure (projected along the c direction), highlighting the FeO6 octahedra sharing edges and corners to build five octahedra long and three octahedra wide zig-zag walls (dark and light green ribbons). O1, O3 and O5 label oxygens of a triangular BO3 unit (boron atoms in pink). (b) Same projection of the structure highlighting the two types of three-leg ladders Fe4-Fe2-Fe4 (3LL1, in blue) and Fe3-Fe1-Fe3 (3LL2, in orange). (c) 3LL1 and 3LL2 ladders with corresponding first-neighbor magnetic exchange paths (JC along the legs, J1 and J2 along the 3LL1 and 3LL2 rungs, respectively), and triangular topology of the J f coupling between 3LL1 and 3LL2.

FIG. 4 .

 4 FIG. 4. (color online) : (a) Upper panel: Mn K-edge absorption spectrum of Fe1.5Mn1.5BO5, the measured spectrum is compared to the reference spectra of MnO (black solid lines) and Mn2O3 (black dashed lines). Lower panel: Mn K-edge absorption spectra of Fe3-xMnxBO5 samples (x = 0.25 to 1.5). The data are shifted vertically for clarity. The two black dashed lines are guide to the eyes to highlight the constant energy position of XANES features for all samples. (b) Fe K-edge absorption spectra of Fe3-xMnxBO5 samples (x = 0 to 1.5). The measured spectra are compared to the reference spectra of FeO (black solid lines) and Fe2O3 (black dashed lines).

FIG. 5 .

 5 FIG. 5. (color online) : Combined Rietveld refinements of the (a) SXRPD (λ = 0.6694 Å) and (b) NPD (λ = 1.4618 Å) data of Fe2MnBO5 at 300 K. Inset of (b) : Low Q enlargement of the NPD pattern, to show the diffuse scattering due to Fe/Mn distribution (λ = 2.426 Å) at 300 K.

FIG. 6 .

 6 FIG. 6. (color online) : Temperature evolution of the zfc and fc magnetic susceptibility χ in 100 Oe in the Fe3-xMnxBO5 system, for x = 0 (a), 0.25 (b), 0.50 (c), 0.75 (d) and x = 1 (e). (f) shows an enlargement of the χ(T) for x = 0.50 around TN1. Arrows show for each composition TN1 (in blue) and TN2 (in red).

FIG. 7 .

 7 FIG. 7. (color online) : (a) Rietveld refinement of the NPD data for x = 1 at 1.5 K. Inset : enlargement of the (0 2 0) peak to illustrate additional magnetic intensity below 35 K. Right panel : Magnetic ordering on 3LL1 (blue) and 3LL2 (orange) depending on the temperature range considered (TN2 ≤ T ≤ TN1 (b) and T ≤ TN2 (c)). (d) Temperature evolution of the NPD patterns of Fe2MnBO5 (left) and corresponding evolution of the refined magnetic moment on each (Fe/Mn) site (e). Blue (red) empty squares indicate the main magnetic Bragg peaks observed below TN1 (TN2) in (d).

FIG. 8 .

 8 FIG. 8. (color online) : ac susceptibility measurements vs. temperature as a function of frequency f (10 Hz to 10 4 Hz) for x = 0.75 and x = 1 in the Fe3-xMnxBO5 system (in 10 Oe).

FIG. 9 .

 9 FIG. 9. (color online) : (a) Magnetic susceptibility (zfc and fc) measurements for x = 1.5 in 100 Oe ; the inset shows corresponding ac susceptibility measurements in the range 10 Hz-10 4 Hz in 10 Oe. (b) Temperature evolution of the ordered magnetic moment on each site for Fe1.5Mn1.5BO5 (from NPD data). TN and T down are shown by black arrows.

FIG. 11 .

 11 FIG. 11. (color online) : (x, T) phase diagram of the Fe3-xMnxBO5 system. TN1 and TN2 (x ≤1) or TN (x > 1) are shown as blue squares, red squares, and green circles, respectively. Tcross and T down are also shown as white triangles pointing up or down, respectively. White stars indicate the onset of ac frequency effects in the susceptibility curves. Arrows indicate x values for which neutron diffraction experiments have been performed. The composition range can be separated into decoupled and coupled magnetic sub-lattices, as highlighted by the blue and green areas, respectively. The grey area shows the x range in which the nature of the magnetic ordering changes. The dark green area remains unexplored. Corresponding magnetic orders are illustrated (see also text).

TABLE III .

 III Selected atomic distances (in Å) at 180 K and 4 K in Fe2MnBO5 (from Rietveld refinement results in the Pbam space group using high resolution NPD data).

		180 K	4 K
	Cell parameters ( Å)
	a	9.5147(3)	9.5064(3)
	b	12.4146(4)	12.4065(4)
	c	3.0870(1)	3.0845(1)
	Cell volume V ( Å3 )	364.6(2)	363.8(2)
	(Fe/Mn)1-O	2.218(8) x4	2.202(9) x4
		2.03(1) x2	2.02(1) x2
	<(Fe/Mn)1-O>	2.16(1)	2.14(1)
	(Fe/Mn)2-O	2.110(6) x4	2.095(7) x4
		2.08(1) x2	2.09(1) x2
	<(Fe/Mn)2-O>	2.10(1)	2.09(1)
	(Fe/Mn)3-O	2.23(1) x2	2.24(2) x2
		2.21(2) x2	2.18(2) x2
		2.06(2)	2.03(2)
		2.10(2)	2.12(2)
	<(Fe/Mn)3-O>	2.17(2)	2.16(2)
	(Fe/Mn)4-O	1.993(7) x2	2.001(7) x2
		2.113(8) x2	2.118(8) x2
		2.06(1)	2.07(1)
		2.12(1)	2.12(1)
	<(Fe/Mn)4-O>	2.06(1)	2.07(1)
	d1-3	3.44(2)	3.47(2)
	d2-4	2.824(7)	2.814(7)
	d2-3	3.17(1)	3.14(1)
	d1-4	3.114(6)	3.122(6)
	d3-4	3.17(2)	3.09(2)

The authors thank S. Dufourd and F. Veillon (CRISMAT) for technical support. This work was supported by the French-Romanian project ANR-UEFISCDI, contracts No. RO-FR/01.01.2013, code PN-II-ID-JRP-2011-2-0056/ANR-12-IS08-0003, COFeIn and the Agence Nationale de la Recherche (ANR-16-CE08-0007-01 contract BORA-BORA). Neutron measurement were performed also at the CANAM infrastructure of the NPI CAS Rez and reactor LVR15 supported through MSMT project No. LM2015056 and LM2015074.


Stephen H Fairclough
email: s.fairclough@ljmu.ac.uk

Fabien Lotte
email: fabien.lotte@inria.fr

Grand Challenges in Neurotechnology and System Neuroergonomics

Keywords: EEG, fNIRS, human-computer interaction, brain-computer interfaces, neurotechnologies, neuroergonomics

INTRODUCTION

The research field of Neuroergonomics aims at "Understanding the brain in the wild, its activity during unrestricted real-world tasks in everyday life contexts, and its relationship to action, behavior, body, and environment" [START_REF] Dehais | Brain in the wild as the next frontier: grand field challenges for neuroergonomics[END_REF]. This field has tremendous potential to develop innovative applications across many fields, such as education, manufacturing, entertainment, health, transportation. In order to achieve this potential, many research applications of Neuroergonomics rely on or require neurotechnologies. Neurotechnology is a category of technology where system design incorporates neural principles or directly interfaces with signals from the brain and body. The most popular types of neurotechnologies notably include Brain-Computer Interfaces (BCI) (Clerc et al., 2016a,b;[START_REF] Nam | Brain-Computer Interfaces Handbook: Technological and Theoretical Advances[END_REF] and Physiological computing [START_REF] Fairclough | Fundamentals of physiological computing[END_REF][START_REF] Fairclough | Advances in Physiological Computing[END_REF]. In order to be used in practice, Neuroergonomics must also be studied and integrated at the whole system level. In other words, we need to develop concepts of Systems Neuroergonomics, an interdisciplinary field of engineering, neuroscience and human factors, which integrates approaches from Neuroergonomics into the design, development, and management of complex systems (e.g., planes, information systems, video games, or medical devices). Systems in this context refers to any combination of machines, robots, computers, and automation with human users. The present journal, Frontiers in Neuroergonomics, section Neurotechonology and System Neuroergonomics, aims to publish significant advances in those principles, protocols, and applications that underpin the development of neurotechnology in the context of Neuroergonomics, i.e., to create novel forms of humancomputer interaction that could enhance, e.g., safety, productivity, or health.

However, this objective remains far from the reality of how technologies are integrated into work and leisure in everyday life. Indeed, the vast majority of neurotechnologies for Neuroergonomics remain at the level of demonstrator systems used for laboratory research, and very few are used outside those laboratories. If Neuroergonomics, by definition, aims at studying behavior and technologies as they are used in the wild, it is important for neurotechnologies to also make this developmental leap from the laboratory and into the real world. Moreover, we must develop a systems understanding of how neurotechnologies may be embedded in the work of the individual, the team, and the organization. In order to understand how neurotechnologies can evolve from their current status as laboratory demonstrators to usage cases in everyday work and leisure, we have proposed three grand challenges: (1) Designing neurotechnologies that are robust and reliable, even outside the lab, with high accuracy across all usage contexts. This is a challenge at the machine level. (2) Designing user experience with neurotechnologies, to ensure that these technologies are usable, acceptable, and useful for its users. This is a challenge at the user level. (3) Developing Systems thinking in Neuroergonomics, to integrate, study, and optimize Neuroergonomics into system design, in a principled way. This is a challenge at the overall system level. These grand challenges are illustrated in Figure 1 and are described in more details in the following sections.

GRAND CHALLENGE: DESIGNING ROBUST AND RELIABLE NEUROTECHNOLOGIES

Despite their potential, current neurotechnologies are still far from being sufficiently reliable for use in everyday work and life. Existing systems make frequent and numerous mistakes in decoding the users' mental states or intentions from their neurophysiological signals [START_REF] Allanson | A research agenda for physiological computing[END_REF][START_REF] Krusienski | Critical issues in state-of-the-art brain-computer interface signal processing[END_REF][START_REF] Lotte | Towards usable electroencephalography-based brain-computer interfaces[END_REF][START_REF] Chavarriaga | Heading for new shores! overcoming pitfalls in BCI design[END_REF][START_REF] Lotte | A review of classification algorithms for EEG-based braincomputer interfaces: a 10-year update[END_REF]. This poor reliability is due to a number of factors, such as imperfect neurophysiological sensors, notably Electroencephalography (EEG) and functional Near Infrared Spectroscopy (fNIRS) which only record relatively low Signal-to-Noise-Ratio (SNR) data. These types of physiological signals are very sensitive to various types of systemic artifacts originating from non-neuronal sources, e.g., muscles (Electromyography-EMG), eyes (Electrooculography-EOG), or motions for EEG [START_REF] Goncharova | EMG contamination of EEG: spectral and topographical characteristics[END_REF][START_REF] Fatourechi | EMG and EOG artifacts in brain computer interface systems: a survey[END_REF] or from various light sources or motions for fNIRS [START_REF] Vitorio | fNIRS response during walking-artefact or cortical activity? A systematic review[END_REF][START_REF] Hocke | Automated processing of fNIRS data-a visual guide to the pitfalls and consequences[END_REF], or from the environment itself [START_REF] Sweeney | Artifact removal in physiological signals-practices and possibilities[END_REF]. This deterioration of neurophysiological signals by artifacts is even more pronounced in real-life situations, with potentially mobile users and noisy environments [START_REF] Lotte | Towards ambulatory brain-computer interfaces: a pilot study with P300 signals[END_REF][START_REF] Strait | What we can and cannot (yet) do with functional near infrared spectroscopy[END_REF][START_REF] Minguillon | Trends in EEG-BCI for daily-life: requirements for artifact removal[END_REF], which also represent the target use case of Neuroergonomics. While various approaches have been proposed to deal with artifacts in the neurophysiological record (see e.g., [START_REF] Cooper | A systematic comparison of motion artifact correction techniques for functional near-infrared spectroscopy[END_REF][START_REF] Sweeney | Artifact removal in physiological signals-practices and possibilities[END_REF][START_REF] Urigüen | EEG artifact removal-state-of-the-art and guidelines[END_REF][START_REF] Jiang | Removal of artifacts from EEG signals: a review[END_REF], these corrective strategies are still far from being perfect and do not remove the whole artifact, i.e., a residual artifact remains, or they risk accidentally removing a relevant part of the signal. Finally, neurophysiological signals are also highly non-stationary with significant variation between different users and within the same user, e.g., between days or even within the same day (see [START_REF] Abu-Alqumsan | Invariance and variability in interaction error-related potentials and their consequences for classification[END_REF][START_REF] Krumpe | Nonstationarity and inter-subject variability of EEG characteristics in the context of BCI development[END_REF][START_REF] Mladenovic | A generic framework for adaptive EEG-based BCI training and operation[END_REF][START_REF] Saha | Intra-and inter-subject variability in EEG-based sensorimotor brain computer interface: a review[END_REF].

The goal of this grand challenge is to design robust neurotechnology that can decode users' states reliably during everyday work and leisure, despite those various sources of noise, artifacts, and non-stationarity that affect the recorded signals. This goal can be decomposed into a number of sub-challenges. The first sub-challenge is to design new sensors that can record neurophysiological signals with higher SNR. In addition, in order to be able to deal with the various sources of noise, artifacts, and non-stationarity, we must be able to build detailed computational models in order to characterize them. What are their spatial, temporal or spectral characteristics? What are their causes? What are their specific influences on neurophysiological signals? Current research has provided partial answers to some of these questions (see, e.g., [START_REF] Grosse-Wentrup | What are the causes of performance variation in brain-computer interfacing?[END_REF][START_REF] Ahn | Performance variation in motor imagery brain-computer interface: a brief review[END_REF][START_REF] Jeunet | Towards a cognitive model of MI-BCI user training[END_REF], but in order to design robust neurotechnologies in an informed way, we require computational models that are detailed and predictive. These types of models would enable us to optimize the design of algorithms to detect noise sources and artifacts for specific signals in a particular context (e.g., task, environment), and allow us to remove them in order to yield "clean" neurophysiological signals. The same knowledge could also be used to design machine learning and signal processing algorithms that are robust to specific sources of artifacts and noise, or even to extract neurophysiological features that are invariant to these noise sources, extending those ideas initiated by [START_REF] Blankertz | Invariant common spatial patterns: alleviating nonstationarities in brain-computer interfacing[END_REF] and [START_REF] Lotte | Regularizing common spatial patterns to improve BCI designs: unified theory and new algorithms[END_REF]. Similarly, models of non-stationarities would enable us to track them more finely, and in doing so, design decoding algorithms that are not strongly influenced by their presence. Alternatively, we could design adaptive machine learning algorithms [START_REF] Shenoy | Towards adaptive classification for BCI[END_REF][START_REF] Lotte | A review of classification algorithms for EEG-based braincomputer interfaces: a 10-year update[END_REF], that would update parameters in an informed way in order to accommodate non-stationarities in their source signals. It is important to note that we would require such algorithms for both off-line data (for off-line evaluations and/or more fundamental neuroscientific studies) but also for their online equivalents, for integration into realtime neurotechnologies. Therefore, another sub-challenge that relates specifically to the online case is the requirement to design algorithms that are sufficiently computationally efficient to be used online.

The design of reliable and robust neurotechnologies also requires the design of algorithms that can exploit available data in an optimal fashion. For example, the design of algorithms based on multimodal data that jointly exploit multiple types of neurophysiological signals within the same process of classification, e.g., combining features from EEG, fNIRS, electrocardiogram (ECG), or galvanic skin response (GSR), in order to amalgamate the particular strengths of each. In other words, we need to design versatile and effective Hybrid BCIs [START_REF] Pfurtscheller | The hybrid BCI[END_REF][START_REF] Banville | Recent advances and open challenges in hybrid brain-computer interfacing: a technological review of non-invasive human research[END_REF]. We also need to design algorithms that can be calibrated or trained with as little data as possible, given how little data is typically available prior to sustained usage by an individual. A classification algorithm that could be efficiently trained (i.e., from little data) would also reduce the calibration times of current neurotechnologies [START_REF] Lotte | Signal processing approaches to minimize or suppress calibration time in oscillatory activity-based brain-computer interfaces[END_REF]. Ideally, the aim for neurotechnologies that are used in everyday life should be removing altogether the need for new data for each new user, using, e.g., transfer learning [START_REF] Jayaram | Transfer learning in brain-computer interfaces[END_REF]. Since neurotechnologies for neuroergonomics often aim at decoding specific mental states, we would need to identify biomarkers that are specific to those mental states, but do not vary with co-existing states, thus ensuring their robust decoding [START_REF] Fairclough | Fundamentals of physiological computing[END_REF]. Finally, in order to be able to design and build all the models and algorithms described in this section, we would need large databases that represent neurophysiological data collected in the field. Therefore, the final sub-challenge would be to collect, build, consolidate, and share large databases of neurophysiological and psychophysiological signals, which have been measured across many users, tasks, contexts, and real operational environments (e.g., in planes or cars).

GRAND CHALLENGE: DESIGNING USER EXPERIENCE WITH NEUROTECHNOLOGIES

Issues associated with the user experience represents a significant challenge for the development of neurotechnologies. This is an important issue because all nascent technologies must offer tangible benefits in order to achieve widespread adoption, and these benefits are manifested via the user experience. The first part of this challenge concerns the design of those peripherals used for neurotechnology. Wearable sensors must be designed for comfort, robustness, aesthetic design, and unobtrusive measurement that does not compromise the quality of data collection [START_REF] Mihajlović | Wearable, wireless EEG solutions in daily life applications: what are we missing[END_REF]. In practice, this balance can be difficult to achieve, especially when sensors must be used over long periods of time in everyday/public environments. As a secondary point, these wearable devices, which are designed to exchange data with other devices, must encompass reliable communication protocols that are easily installed by members of the general public.

While neurotechnology has enormous potential to enhance human-computer interaction (HCI) by expanding communication bandwidth and developing personalized modes of interaction, acceptance depends largely on which adaptive strategies are deployed [START_REF] Fuchs | Session overview: adaptation strategies and adaptation management[END_REF] and users' perceptions of their utility and effectiveness. At the present time, we know relatively little about the level of system error that is acceptable to users when they interact with neurotechnology (Évain et al., 2016). When errors do occur, error recovery mechanisms must be seamlessly integrated into the interaction with the user. Similarly, we lack a strong understanding of how classification rates derived from machine learning algorithms regarding the internal state of the user correspond with those subjective types of self-assessment that informs perceived accuracy of the system [START_REF] Fairclough | Classification accuracy from the perspective of the user: real-time interaction with physiological computing[END_REF][START_REF] Mccrea | Absolute and relative user perception of classification accuracy in an affective video game[END_REF]. Due to the high speed of data exchange between brain and machine, interactions with neurotechnology can occur implicitly and autonomously, i.e., functions can be activated without seeking confirmation from the user [START_REF] Solovey | Designing implicit interfaces for physiological computing: guidelines and lessons learned using fNIRS[END_REF][START_REF] Serim | Explicating "implicit interaction": An examination of the concept and challenges for research[END_REF]. While this is a potentially exciting development from a HCI perspective, we know relatively little about how users will respond to this type of interaction mechanic, will they welcome an opportunity to communicate unconsciously with a machine or experience the triggering of autonomous functions by real-time changes in neurophysiological activity as a loss of personal control?

Research into interface design principles for neurotechnologies remains largely unexplored with the exception of active control BCI [START_REF] Mason | A general framework for braincomputer interface design[END_REF][START_REF] Zander | Towards passive brain-computer interfaces: applying brain-computer interface technology to human-machine systems in general[END_REF]. The provision of feedback to the user is a particularly important component of interface design. Feedback allows users to understand the internal contingencies of the system [START_REF] Pillette | Redefining and adapting feedback for mental-imagery based brain-computer interface user training to the learners' traits and states[END_REF], but given the high-throughput of data during these interactions, how can feedback be delivered at the interface without overwhelming the individual with information? From the perspective of the user, working with a neurotechnology is a learning experience that unfolds over a sustained period of use; but at the time of writing, we have very little understanding of how this longitudinal dimension influences user behavior. If users receive neurophysiological feedback over a sustained period of repeated interactions, it is possible for them to learn how to self-regulate brain activity in order to achieve a desired outcome, as would be the case with conventional neurofeedback; however, we are currently unable to assess the viability of self-regulation as an interaction mechanic beyond the mental and motor imagery protocols, which characterize active BCI [START_REF] Cavazza | Integrating virtual agents in BCI neurofeedback systems[END_REF]. Similarly, sustained exposure to a working neurotechnology permits the user to assess an appropriate degree of trust in the system, which is likely to be highly significant for those systems associated with autonomous function [START_REF] Lee | Trust in automation: designing for appropriate reliance[END_REF][START_REF] Hoff | Trust in automation: Integrating empirical evidence on factors that influence trust[END_REF] and can be assessed using psychophysiological [START_REF] Hu | Real-time sensing of trust in human-machine interactions[END_REF] and neurophysiological [START_REF] De Visser | Learning from the slips of others: neural correlates of trust in automated agents[END_REF] measures.

The evaluation of working neurotechnology presents another set of challenges for the researcher. The whole purpose of this technology is to enhance or extend existing modalities of human-machine communication. In order to demonstrate that HCI have been improved or enhanced, neurotechnology must be evaluated, but this type of assessments is relative and must be benchmarked to an appropriate point of comparison. The development of methodologies and measures to permit the evaluation of neurotechnology remains mostly unexplored [START_REF] Chavarriaga | Heading for new shores! overcoming pitfalls in BCI design[END_REF]. There is a past precedent for using randomized inputs or "yoked" controls for the purposes of comparison [START_REF] Scerbo | A brain-based system for adaptive automation[END_REF][START_REF] Zander | Neuroadaptive technology enables implicit cursor control based on medial prefrontal cortex activity[END_REF] but these methods await consolidation within a generic framework for the evaluation of neurotechnology. Metrics for evaluation remain at a similar level of immaturity and these metrics can be complex for systems that blur the traditional distinction between user and technology [START_REF] Fairclough | A closed-loop perspective on symbiotic human-computer interaction[END_REF]. A working neurotechnology represents a hybrid system where human and machine operate as a single "cooperative intelligent entity" (p. 96) [START_REF] Hancock | Mind, Machine and Morality: Towards a Philosophy of Human-Technology Symbiosis[END_REF]. The generative interplay between "live" neurophysiological data and the adaptive logic of technology lies at the crux of user interaction and is quantified by observing the behavior of the system; hence the behavior of the adaptive system itself represents a central metric for system evaluation [START_REF] Ewing | Evaluation of an adaptive game that uses EEG measures validated during the design process as inputs to a biocybernetic loop[END_REF].

GRAND CHALLENGE: SYSTEMS THINKING IN NEUROERGONOMICS

A systems perspective on the development of neurotechnology can be understood at two levels of analyses. In the first instance, neurotechnology work on a closed-loop basis wherein data is collected from the user, transformed and relayed to the individual via events at the interface. This type of biocybernetic system [START_REF] Pope | Biocybernetic system evaluates indices of operator engagement in automated task[END_REF] is characterized as a control loop where the boundary between person and machine is rendered porous to enable a symmetrical mode of human-computer interaction [START_REF] Hettinger | Neuroadaptive technologies: applying neuroergonomics to the design of advanced interfaces[END_REF]. This bidirectional exchange of data can be extended by incorporating concepts from neural function and neural architecture into the technical specification and design of the system. For example, deep learning is a machine learning method designed to emulate representational learning in a way that parallels computation in the brain; this method has been incorporated into the design of BCI [START_REF] Roy | Deep learning-based electroencephalography analysis: a systematic review[END_REF][START_REF] Zhang | A survey on deep learning based brain computer interface: recent advances and new frontiers[END_REF] and there may be other features of neural computation that will transfer to the design of neurotechnology.

The second challenge involves broadening the context of system usage to consider neurotechnology as a sociotechnical system. If neurotechnology is to be widely adopted, it is important to anticipate how it may function for different users operating across multiple contexts (e.g., work vs. leisure) and being subject to those legal/governance issues that operate in the real-world. At the current time, research on neurotechnology tends to ignore this broad context, although there are exceptions (e.g., IEEE, 2020). Neurotechnology must operate within a sociotechnical hierarchy that includes protocols and procedures defined by managements, companies, regulators, and government [START_REF] Rasmussen | Risk management in a dynamic society: a modelling problem[END_REF]. The influence of this hierarchy is impossible to reproduce in the laboratory and sociotechnical issues must be studied "in the wild" using real employees incorporating neurotechnology into existing work practices [START_REF] Wilson | Fundamentals of systems ergonomics/human factors[END_REF]. Understanding the influence of the sociotechnical hierarchy on the design, functionality and usage of neurotechnology is an important challenge for the field in general and the development of commercial systems in particular.

By expanding our conception of how neurotechnology works to include real-world constraints, we are striving to "futureproof " system concepts and working prototypes. Interactions between neurotechnologies and other components, which may be social, organizational, economic, or political in nature, can only be observed in the real world. In addition, the closed-loop character of neurotechnology already occupies the boundary between a complicated system (i.e., a system that is difficult to understand but can be decomposed) and a complex one (i.e., a system that can evolve behavior and behave in ways unanticipated by the designer). The "darkness principle" [START_REF] Siemieniuch | Systems integration[END_REF] states that "no system can be known completely" and this principle is pertinent to the adoption and utilization of neurotechnology in the field across various settings and tasks. In addition to patterns of unanticipated usage that are often observed under real-world constraints of time, space, protocols, and procedures [START_REF] Wilson | Fundamentals of systems ergonomics/human factors[END_REF], there are various ways in which the technical properties of the system can influence procedures in a bottom-up direction at the higher levels of sociotechnical hierarchy, e.g., requirement for new processes or laws. This complexity requires the researcher to maintain a holistic perspective, understanding how neurotechnology influences health, duration of working hours, liability for error etc. as well as the traditional emphasis on performance efficiency. This perspective also represents a tacit argument for a participatory design approach wherein prospective users have an opportunity to experience the system and provide feedback on how neurotechnology should be designed and integrated into work or lifestyle practices.

SUMMARY AND CONCLUSIONS

In this article, we have considered the challenges of developing robust categories of neurotechnology that can be utilized in the real-world. These systems range from active BCI to passive forms of neuroadaptive technologies, and encompass related system that incorporate measurement of peripheral physiology, such as physiological computing and affective computing. These systems are united by the need for wearable sensors, a requirement to assess the cognitive/emotional state of the user in real-time and a bidirectional flow of information between user and system that can be described as a closed-loop. If neuroergonomics represents the study of the brain in the context of everyday life, neurotechnology extends this approach by turning those lessons learned from that field of study into novel forms of communication between user and system. However, there are numerous challenges facing the successful transition of this nascent technology from the laboratory into working systems that are utilized by people on an everyday basis. Methods for measuring neurophysiology and psychophysiology were developed originally for use under controlled conditions, the first grand challenge for neurotechnology is the creation of sensors combined with mathematical methods that can deliver robust data in the real-world. If this challenge was achieved and we could obtain accurate neurophysiological data from everyday life, the next problem involves a conversion of that technical achievement into novel modes of human-computer interaction that offer genuine utility for the user. In other words, neurotechnology should enhance performance or health or enjoyment in a way that is genuinely beneficial and cannot be achieved by some other means. The benefits of using neurotechnology must be both tangible and unique. In order to explore how neurotechnology can create positive user experiences, we must develop our understanding of longitudinal use, the development of trust and the design of appropriate methods to enable system evaluation. Once we have a robust neurotechnology that seems to deliver real utility for a specific user or groups of user, it is important to consider the sociotechnical context of system use with respect to organizational, economic, and political structures. Standards of governance for neurotechnologies can be informed by recommendations for ethical AI [START_REF] Dib | AI Principles: Recommendations on the Ethical Use of Artificial Intelligence by the Department of Defense[END_REF]. Neurotechnology requires privileged access to data sources that are covert, rich and sensitive to a variety of influences and it is important that standards of governance and data privacy keep pace with practices if this emergent technology is adopted at scale.

FIGURE 1 |

 1 FIGURE 1 | A graphic illustration of the three grand challenges (GC) for Neurotechnology and Systems Neuroergonomics.

Frontiers in Neuroergonomics | www.frontiersin.org

November 2020 | Volume 1 | Article 602504

FUNDING

FL was partly supported by funding from the European Research Council with project BrainConquest (grant ERC-2016-STG-714567).

AUTHOR CONTRIBUTIONS

All authors contributed equally to the intellectual efforts and writing of the paper.

Conflict of Interest:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.