I Gross

W Akhtar

V Garcia

L J Martínez

S Chouaieb

K Garcia

C Carrétéro

A Barthélémy

P Appel

P Maletinsky

J.-V Kim

J Y Chauleau

N Jaouen

M Viret

M Bibes

S Fusil

V Jacques

Real-space imaging of non-collinear antiferromagnetic order with a single spin magnetometer

While ferromagnets are at the heart of daily life applications, their large magnetization and resulting energy cost for switching bring into question their suitability for reliable lowpower spintronic devices. Non-collinear antiferromagnetic systems do not suffer from this problem and often possess remarkable extra functionalities: non-collinear spin order 1 may break space-inversion symmetry 2, 3 and thus allow electric-field control of magnetism 4, 5 , or produce emergent spin-orbit effects 6 which enable efficient spin-charge interconversion 7 .

 . In addition, we take advantage of the magnetoelectric coupling present in BiFeO 3 to manipulate the cycloid propagation direction by an electric field. Besides highlighting the unique potential of NV magnetometry for imaging complex antiferromagnetic orders at the nanoscale, these results demonstrate how BiFeO 3 can be used as a versatile platform for the design of reconfigurable nanoscale spin textures.

Nearly 90% of known magnetic materials have dominant antiferromagnetic interactions, resulting in no or very small magnetization, and most are also insulators 1 . This strongly impedes their investigation, especially when the magnetic order needs to be mapped at the nanoscale. While

magnetic force microscopy [START_REF] Hartmann | Magnetic force microscopy[END_REF] or X-ray photoemission electron microscopy [START_REF] Locatelli | Recent advances in chemical and magnetic imaging of surfaces and interfaces by XPEEM[END_REF] can reach a spatial resolution of a few tens of nm, their sensitivities are not compatible with the detection of weak magnetic signals commonly involved in antiferromagnets. Spin-polarized scanning tunnelling microscopy can resolve the magnetic moments of single atoms [START_REF] Wiesendanger | Spin mapping at the nanoscale and atomic scale[END_REF] but is only applicable to conductive systems. Therefore, the spin texture of the vast majority of magnetically ordered materials cannot be directly imaged at the nanoscale. This is increasingly problematic since materials with complex antiferromagnetic orders show very appealing functionalities, which are absent in ferromagnets, and start to be exploited in a new generation of low-power spintronic devices [START_REF] Jungwirth | Antiferromagnetic spintronics[END_REF] .

Typical examples are multiferroics, in which antiferromagnetism coexists with ferroelectricity, enabling an efficient electrical control of magnetization through magnetoelectric coupling [START_REF] Cheong | Multiferroics: a magnetic twist for ferroelectricity[END_REF][START_REF] Lottermoser | Magnetic phase control by an electric field[END_REF][START_REF] Heron | Deterministic switching of ferromagnetism at room temperature using an electric field[END_REF] .

Bismuth ferrite BiFeO 3 (BFO) is such a multiferroic material [START_REF] Catalan | Physics and applications of bismuth ferrite[END_REF] , which is currently emerging as a unique platform for spintronic [START_REF] Heron | Deterministic switching of ferromagnetism at room temperature using an electric field[END_REF] and magnonic devices [START_REF] Rovillain | Electric-field control of spin waves at room temperature in multiferroic BiFeO 3[END_REF] because its multiferroic phase is preserved well above room temperature. However, while the ferroelectric properties of BFO have been widely investigated by piezoresponse force microscopy (PFM), revealing unique domain structures and domain wall functionalities [START_REF] Balke | Enhanced electric conductivity at ferroelectric vortex cores in BiFeO 3[END_REF][START_REF] Catalan | Domain wall nanoelectronics[END_REF] , the corresponding nanoscale magnetic textures and their potential for spin-based technology still remain concealed. In this work we demonstrate the first real-space imaging and electric field manipulation of complex antiferromagnetic order in a BFO thin film by using an atomic-sized magnetometer based on a single NV defect in diamond.

Bulk BFO crystallizes in a slightly-distorted rhombohedral structure, but is commonly described by the pseudocubic unit cell shown in Fig. 1a. The displacement of Bi ions relative to the FeO 6 octahedra gives rise to a strong ferroelectric polarization (100 µC/cm 2 ) along one of the

[111] directions 17 . This system is complex as the eight possible polarization orientations P ± i give rise to three types of ferroelectric domain walls (71 • , 109 • , or 180 • ). From the magnetic point of view, BFO was initially thought to be a conventional G-type antiferromagnet [START_REF] Park | Structure and spin dynamics of multiferroic BiFeO 3[END_REF] but high-resolution neutron diffraction later revealed a cycloidal antiferromagnetic order [START_REF] Sosnowska | Spiral magnetic ordering in bismuth ferrite[END_REF][START_REF] Lebeugle | Electric-Field-Induced Spin Flop in BiFeO 3 Single Crystals at Room Temperature[END_REF] with a characteristic wavelength of λ ∼ 64 nm [Fig. 1b]. The spin cycloid propagation direction and the ferroelectric polarization vector are normal to each other and are linked by magnetoelectric coupling. In addition, the rhombohedral symmetry of BFO allows three equivalent propagation directions of the cycloid (k 1 , k 2 , k 3 ) for a given variant of ferroelectric domain [START_REF] Lebeugle | Electric-Field-Induced Spin Flop in BiFeO 3 Single Crystals at Room Temperature[END_REF][START_REF] Park | Structure and spin dynamics of multiferroic BiFeO 3[END_REF] [Fig. 1c].

A 32-nm-thick BFO(001) film was grown by pulsed laser deposition on a DyScO 3 (110) orthorhombic substrate, using an ultrathin buffer electrode of SrRuO 3 [cf. Methods and Extended Data Fig. 1]. Epitaxial strain leads to an array of striped ferroelectric domains whose typical width is in the range of ∼ 100 nm [Fig. 1d]. In-depth PFM and X-ray diffraction analysis reveal that only two variants of polarization coexist [P - 3 and P - 4 in Fig. 1d], separated by 71 • domain walls [cf. Methods and Extended Data Fig. 2 and3]. In thin films the spin cycloid can be modulated or even destroyed by epitaxial strain. Considering the low lattice mismatch between BFO and DSO (∼ 0.4%), the cycloidal antiferromagnetic order is however expected to be preserved in the studied epitaxial thin film [START_REF] Sando | Crafting the magnonic and spintronic response of BiFeO 3 films by epitaxial strain[END_REF] .

The spin texture of the BFO sample was investigated through stray field measurements using a scanning nanomagnetometer based on a single NV defect in diamond [START_REF] Maze | Nanoscale magnetic sensing with an individual electronic spin in diamond[END_REF][START_REF] Balasubramanian | Nanoscale imaging magnetometry with diamond spins under ambient conditions[END_REF][START_REF] Rondin | Magnetometry with nitrogen-vacancy defects in diamond[END_REF] . This point-like impurity can be exploited for quantitative magnetic field imaging at the nanoscale by recording Zeeman shifts of its electronic spin sublevels through optical detection of the electron spin resonance (ESR). For the present study, a single NV defect placed at the apex of a nanopillar in a diamond scanning-probe is integrated into an atomic force microscope, which allows scanning the NV defect in close proximity to a sample [START_REF] Maletinsky | A robust scanning diamond sensor for nanoscale imaging with single nitrogen-vacancy centres[END_REF] which is simply given by ∆ z = γ e B NV /2π, where γ e /2π = 28 GHz/T is the electronic spin gyromagnetic ratio and B NV is the magnetic field projection along the NV defect quantization axis.

The resulting magnetic sensitivity is in the range of a few µT/ √ Hz, while the spatial resolution is fixed by the distance d between the sample and the NV spin sensor [START_REF] Rondin | Magnetometry with nitrogen-vacancy defects in diamond[END_REF] . This key parameter is independently measured through a calibration process above the edges of an uniformly magnetized ferromagnetic wire [START_REF] Tetienne | The nature of domain walls in ultrathin ferromagnets revealed by scanning nanomagnetometry[END_REF] , leading to d = 49.0±2.4 nm [cf. Methods and Extended Data Fig. 4]. In the following, all experiments are performed under ambient conditions with a bias field B b = 1.4 mT applied along the NV defect axis in order to determine the sign of the measured magnetic fields [START_REF] Rondin | Magnetometry with nitrogen-vacancy defects in diamond[END_REF] .

Such a bias field is weak enough not to modify the magnetic order in BFO.

The scanning-NV magnetometer was first operated in the dual-iso-B imaging mode by monitoring the signal S =PL(ν 2 )-PL(ν 1 ), corresponding to the difference of PL intensity for two fixed RF frequencies, ν 1 and ν 2 , applied consecutively at each point of the scan 10 [Fig. 2b]. A typical dual-iso-B image recorded above the (001)-oriented BFO thin film is shown in Fig. 2c. We observe 3b]. Importantly, the (001) surface projection of the spin cycloid propagation direction is normal to that of the ferroelectric polarization vector P + 1 . Among the three possible cycloid propagation directions, only k 1 is normal to the (001) projection of P + 1 , the other two lying at 45 • from the polarization vector [see inset in Fig. 3c]. We therefore conclude that the spin cycloid propagates along k 1 , i.e. in the plane of the BFO thin film. This result can be qualitatively explained by considering that epitaxial strain modifies the anisotropy along the film normal [START_REF] Sando | Crafting the magnonic and spintronic response of BiFeO 3 films by epitaxial strain[END_REF] . For BFO thin films grown on DSO, compressive strain induces an easy-plane contribution which stabilizes magnetic structures with their spins far from the [001] direction. Thus, the three possible cycloidal directions see their degeneracy lifted and the one propagating along [ 110] becomes energetically favorable [START_REF] Sando | Crafting the magnonic and spintronic response of BiFeO 3 films by epitaxial strain[END_REF] .

Using a two-dimensional fit of the magnetic image with a sinusoidal function, we infer a characteristic wavelength λ = 70.6 ± 1.4 nm [Fig. 3c]. The slightly enhanced period compared to the bulk

Distance [nm]
NV images PFM images value (∼ 64 nm) is interpreted as due to the small compressive strain imposed by the substrate [START_REF] Agbelele | Strain and Magnetic Field Induced Spin-Structure Transitions in Multiferroic BiFeO 3[END_REF] .

This result illustrates that the local magnetoelectric interaction between neighbouring atoms at the origin of the spin cycloid does not require thick films of BFO, i.e. with thicknesses well above its characteristic wavelength, as previously speculated [START_REF] Bertinshaw | Direct evidence for the spin cycloid in strained nanoscale bismuth ferrite thin films[END_REF] .

After demonstrating that the polarization and the cycloid propagation are intimately linked, we intend to manipulate electrically this cycloid propagation direction using the magnetoelectric coupling. To this end, we define another ferroelectric domain with an in-plane component of the polarization rotated by 90

• [P - 4 in
m eff (r ) = m eff [cos(k 1 • r )e k 1 + sin(k 1 • r )e P ] . (1)
Here ||k 1 || = 2π/λ, r denotes the coordinate in the BFO sample, while e k 1 and e P are orthogonal unit vectors oriented along the cycloid propagation direction k 1 and the ferroelectric polarization P, respectively [see Fig. 4b]. The uncompensated magnetic moment per Fe atom is given by

m eff = m Fe sin(α c /2)
, where m Fe = 4.1 µ B is the measured magnetic moment of Fe atoms in BFO at room temperature [START_REF] Lebeugle | Electric-Field-Induced Spin Flop in BiFeO 3 Single Crystals at Room Temperature[END_REF] and α c is the canting angle between antiferromagnetically coupled Fe atoms [Fig. 1b]. This angle is directly deduced from the measured cycloid wavelength, leading to

α c = 2 • and m eff = 0.07 µ B [cf. Methods].
The Dzyaloshinskii-Moriya (DM) interaction resulting from the alternate rotation of the FeO 6 octahedra along the [111] direction is another source of non compensation of the magnetic moments in BFO [START_REF] Park | Structure and spin dynamics of multiferroic BiFeO 3[END_REF][START_REF] Ederer | Weak ferromagnetism and magnetoelectric coupling in bismuth ferrite[END_REF] . In the homogeneous G-type state obtained at high magnetic fields (> 20 T), this effect is known to generate a weak and uniform magnetization. In the cycloidal state, this magnetization is converted into a spin density wave (SDW) oscillating in the [11 2] direction, which leads to a periodic wiggling of the cycloidal plane [START_REF] Ramazanoglu | Local Weak Ferromagnetism in Single-Crystalline Ferroelectric BiFeO 3[END_REF] . As sketched in Fig. 4b, the SDW can be simply modeled by an additional uncompensated magnetization vector

M DM = m DM /V such that m DM (r ) = m DM cos(k 1 • r )(e k 1 × e P ) . (2)
The value of the SDW amplitude m DM still remains debated. Although it is often considered small (∼ 0.03 µ B ) or even negligible [START_REF] Park | Structure and spin dynamics of multiferroic BiFeO 3[END_REF] , polarized neutron scattering studies have revealed a maximum amplitude of 0.09 µ B in bulk BFO [START_REF] Ramazanoglu | Local Weak Ferromagnetism in Single-Crystalline Ferroelectric BiFeO 3[END_REF] , which is slightly larger than the uncompensated moment m eff due to the pure cycloid.

An analytical calculation of the stray field produced above the BFO sample is given in Methods. We postulate here that the magnetic structure generating the stray field is a wriggling cycloid as described elsewhere [START_REF] Park | Structure and spin dynamics of multiferroic BiFeO 3[END_REF][START_REF] Ramazanoglu | Local Weak Ferromagnetism in Single-Crystalline Ferroelectric BiFeO 3[END_REF] . The magnetic potential Φ produced by the magnetization pattern M = M DM + M eff is first calculated using Fourier methods for a monolayer of the BFO sample [START_REF] Mikuszeit | Magnetostatics and the rotational sense of cycloidal spin spirals[END_REF] .

The resulting magnetic field is given by B m = -∇Φ and the total field B produced at a distance z above the BFO sample surface is finally obtained by summing the contribution from each monolayer. In the laboratory frame (x, y, z) [cf. Extended Data Fig. 5], the stray field components are given by

                 B x (r) = -A e -k 1 z [C 1 m eff cos(k 1 • r) -C 2 m DM sin(k 1 • r)] B y (r) = A e -k 1 z [C 1 m eff cos(k 1 • r) -C 2 m DM sin(k 1 • r)] B z (r) = √ 2A e -k 1 z [C 1 m eff sin(k 1 • r) + C 2 m DM cos(k 1 • r)] , (3)
where

C 1 = 1 + 1/ √ 3, C 2 = 2/ √ 6, and
A = µ 0 √ 2V 1 -e -k 1 t 1 -e -k 1 a sinh( ak 1 2 ) . ( 4
)
Here a is the thickness of a BFO monolayer and t the total thickness of the sample. These magnetic field components are then projected along the independently measured NV defect axis in order to obtain an analytical formula for B NV . This formula was used to perform a two-dimensional fit of the experimental data while using m DM as the only fitting parameter [Fig. 4c]. A thorough analysis of uncertainties is given in Methods, including those related to (i) the fitting procedure itself, (ii) the probe-to-sample distance d, (iii) the cycloid wavelength λ, (iv) the sample thickness t and (v) the NV defect orientation. This study leads to m DM = 0.16 ± 0.06 µ B , where the overall uncertainty of ∼ 40% mainly results from the imperfect knowledge of the probe-to-sample distance [Extended Data Fig. 6c]. We note that the stray field produced above the BFO sample also depends on the chirality of the spin cycloid [START_REF] Mikuszeit | Magnetostatics and the rotational sense of cycloidal spin spirals[END_REF] . Equation ( 3) is obtained for a spin cycloid with a counter-clockwise chirality. A similar analysis performed for a clockwise chirality would lead to a larger amplitude of the SDW, m DM = 0.21 ± 0.08 µ B [see Methods]. In both cases, our study suggests a DM interaction significantly stronger than all reported values in the literature.

This result could be explained by considering that the DM interaction is enhanced by the abrupt broken inversion symmetry occurring at the sample surface and then propagated in the BFO thin film by exchange interaction. This observation opens many perspectives for studying emergent interface-induced magnetic interactions resulting from a local breaking of inversion symmetry.

In summary, we have reported the first real-space imaging and electric-field control of the cycloidal antiferromagnetic order in a BFO thin film using a scanning-NV magnetometer operating under ambient conditions. These results open new perspectives for unravelling intriguing phenomena occurring in multiferroic materials like BFO, from magnetoelectric coupling [START_REF] Heron | Deterministic switching of ferromagnetism at room temperature using an electric field[END_REF] , peculiar properties induced by surface symmetry breaking, to conduction and magnetotransport properties at ferroelectric domain walls [START_REF] Balke | Enhanced electric conductivity at ferroelectric vortex cores in BiFeO 3[END_REF][START_REF] He | Magnetotransport at Domain Walls in BiFeO 3[END_REF] . On a broader perspective, NV magnetometry appears as a unique tool for studying the antiferromagnetic order at the nanoscale. In this way, similar investigations could be extended to a myriad of non-collinear antiferromagnetic materials, or to the domain walls

Correspondence Correspondence should be addressed to V. J. (email: vincent.jacques@umontpellier.fr).

Methods

Sample growth. The epitaxial thin film heterostructure was grown by pulsed laser deposition using a KrF excimer laser (λ = 248 nm, 1 J.cm When the cantilever is aligned along [110] c [Extended Data Fig. 3f)], the P - 2 and P - 4 in-plane responses are turned off and all responding domains (bright amplitude in Extended Data Fig. 3g) are pointing to the left side of the cantilever (light phase signal in Extended Data Fig. 3h), identifying P - 3 domains. When the cantilever is aligned along [ 110] c (Extended Data Fig. 3i), the P - 1 and P - 3 in-plane responses are turned off and all responding domains (bright amplitude in Extended Data Fig. 3j) are pointing to the right of the cantilever (dark phase in Extended Data Fig. 3k), identifying P - 4 domains. Note that Extended Data Fig. 3g and 3j show complementary responses so that the ferroelectric configuration in BFO thin films that we presented in the manuscript is determined as alternated P - 3 and P - 4 variants in the form of stripes separated by 71 • domain walls.

In written areas [Fig. 3a,d], single ferroelectric domains are reproducibly obtained: the out-of-plane component of the polarization is controlled by the above coercive bias applied between the scanning tip and the bottom SrRuO 3 electrode. Moreover, the in-plane component is simultaneously defined thanks to the trailing field induced by the tip motion along the slow scan axis and aligned along the targeted polarization variant [START_REF] Balke | Deterministic control of ferroelastic switching in multiferroic materials[END_REF][START_REF] Crassous | Polarization charge as a reconfigurable quasidopant in ferroelectric thin films[END_REF] .

Scanning-NV magnetometry. The experimental setup is described in details in Ref. so that the magnetic potential can be expressed as

Φ(x, y, z) = - µ 0 4π z =+a/2 z =-a/2 (M x * ∂ ∂x 1 r 0 ) + (M y * ∂ ∂y 1 r 0 ) + (M z * ∂ ∂z 1 r 0 ) dz . (9)
where

1 r 0 = 1 x 2 + y 2 + (z -z ) 2 (10)
and M x , M y , M z are the components of the magnetization.

Taking the Fourier transform of Eq. ( 9) and using the convolution theorem

F[f * g] = F [f ]F[g], we obtain F(Φ) = - µ 0 4π z =+a/2 z =-a/2 F(M x )F( ∂ ∂x 1 r 0 ) + F(M y )F( ∂ ∂y 1 r 0 ) + F(M z )F( ∂ ∂z 1 r 0 ) dz . (11)
Here M x , M y and M z involve sine and cosine terms whose Fourier transform are given by Dirac δ function.

The Fourier transform of the ( 1 r ) terms can be obtained by following the procedure described in Ref. 41.

The magnetic potential produced by a monolayer of the sample is finally obtained through an inverse Fourier transform leading to

Φ(x, y, z) = µ 0 sinh(ak 1 /2) V k 1 e -k 1 z C 1 m eff sin(k 1 • r) + C 2 m DM cos(k 1 • r) (12)
where

C 1 = 1 + 1/ √ 3 and C 2 = 2/ √ 6.
The stray magnetic field B m produced at a distance z above a monolayer was then calculated using the relation B m = -∇Φ. The resulting stray field components are given by

                   B m x = - µ 0 sinh(ak 1 /2) √ 2V e -k 1 z C 1 m eff cos(k 1 • r) -C 2 m DM sin(k 1 • r) B m y = + µ 0 sinh(ak 1 /2) √ 2V e -k 1 z C 1 m eff cos(k 1 • r) -C 2 m DM sin(k 1 • r) B m z = + µ 0 sinh(ak 1 /2) V e -k 1 z C 1 m eff sin(k 1 • r) + C 2 m DM cos(k 1 • r) . (13)
Analysis of uncertainties. We now analyze the uncertainty on the fit outcome m DM , which results (i) from the fitting procedure and (ii) from uncertainties on the parameters p i = {λ, m eff , t, d, θ, φ} that are involved in the expression of B NV . In the following, the parameters p i are expressed as p i = pi + σ p i where pi denotes the nominal value of parameter p i and σ p i its standard error. These parameters, which are summarized in Extended Data Fig. 6c, are evaluated as follows :

• The cycloid wavelength λ can be precisely extracted through an independent two-dimensional fit of the experimental data with a simple sinusoidal function. We obtain λ = 70.0 ± 1.4 nm for the quantitative magnetic field image shown in Figure 4. The uncertainty (∼ 2%) comes from the calibration of the (x, y) scanner.

• From the measured cycloid wavelength, we infer a characteristic canting angle of 360 • The NV defect quantization axis is measured by recording the ESR frequency as a function of the amplitude and orientation of a calibrated magnetic field, leading to spherical angles (θ = 128±1 • , φ = 80 ± 1 • ) in the laboratory frame (x, y, z).

• The probe-to-sample distance d is inferred through a calibration measurement described in the previous section, leading to d = 49.0 ± 2.4 nm.

We first evaluate the uncertainty of the fitting procedure. To this end, a two-dimensional fit of the experi-mental data was performed with Equation ( 17) while fixing all the parameters p i to their nominal values pi , leading to m DM = 0.160 ± 0.002 µ B . The relative uncertainty linked to the fitting procedure is therefore given by fit = 1.2%. We note that the intrinsic accuracy of the magnetic field measurement is in the range of δB NV ∼ 10 µT. This leads to an uncertainty of the SDW amplitude δm DM ∼ 0.01 µ B , corresponding to a relative uncertainty m = 6%.

In order to estimate the relative uncertainty p i introduced by each parameter p i , the two-dimensional fit was performed with one parameter p i fixed at p i = pi ± σ p i , all the other five parameters remaining fixed at their nominal values. The corresponding fit outcomes are denoted m DM ( pi + σ p i ) and m DM ( piσ p i ). The relative uncertainty introduced by the errors on parameter p i is then finally defined as

p i = m DM ( pi + σ p i ) -m DM ( pi -σ p i ) 2m DM ( pi ) . (18)
This analysis was performed for each parameter p i and the resulting uncertainties p i are summarized in Extended Data Fig. 6c. The cumulative uncertainty is finally given by

= 2 fit + 2 m + i 2 p i , (19)
where all errors are assumed to be independent.

We finally obtain = 41% and m DM = 0.16 ± 0.06 µ B . We note that the dominating source of uncertainty is given by the imperfect knowledge of the probe-to-sample distance ( d = 39%).

Comparison with numerical simulations. The only assumption used for the calculation of the stray field above the BFO sample consists in considering a two-dimensional spin texture with infinite size in the (x , y ) plane [cf. Extended Data Fig. 5]. Such an assumption is valid since the typical dimension of the ferroelectric monodomain is in the range of 1 µm, which is much larger than the probe-to-sample distance d. This was further verified by comparing the result of the calculation with numerical simulations. To this end, the wall. In this work, postulating either chirality leads to the similar conclusion that the DM interaction is significantly stronger than all reported values in the literature.

Extended Data Figure 4 | Measurement of the probe-to-sample distance. a, The scanning-NV magnetometer is used to measure the magnetic field (grey arrows) produced at the edges of an uniformly magnetized ferromagnetic wire (blue arrows). b, Typical Zeeman-shift profile measured by scanning the NV defect across the edges of a 500-nm-wide wire of Pt/Co(0.6nm)/AlO x with perpendicular magnetic anisotropy. The markers are experimental data and the red solid line is data fitting from which d is extracted [START_REF] Tetienne | The nature of domain walls in ultrathin ferromagnets revealed by scanning nanomagnetometry[END_REF][START_REF] Hingant | Measuring the Magnetic Moment Density in Patterned Ultrathin Ferromagnets with Submicrometer Resolution[END_REF] . We note that only the absolute value of the magnetic field is measured in this experiment.

Figure 1 : 3 and P - 4 )

 134 Figure 1: Ferroelectric and magnetic order in BiFeO 3 . a, Pseudocubic unit cell of BiFeO 3

  [Fig. 2a]. At each point of the scan, optical illumination combined with radiofrequency (RF) excitation enable measuring the ESR spectrum of the NV defect by recording its spin-dependent photoluminescence (PL) intensity [Fig. 2b]. Any magnetic field emanating from the sample is then detected through a Zeeman shift of the ESR frequency,

Figure 2 :

 2 Figure 2: Mapping the magnetic texture of BiFeO 3 with NV magnetometry. a, The electronic

1

 1 Norm. iso-B signal Norm. iso-B signal

Figure 3 :

 3 Figure 3: Electrical control of the spin cycloid. a, d, In-plane PFM images of ferroelectric

  Fig. 1d]. The magnetic image shows that the propagation direction of the spin cycloid is also rotated by 90 • with a very similar wavelength λ = 71.4 ±1.4 nm, once again corresponding to the propagation direction k 1 lying in the (001) plane [Fig. 3e,f]. These experiments illustrate how magnetoelectric coupling can be used to efficiently control and manipulate the antiferromagnetic order in a BFO thin film. They also confirm that the abrupt rotations of the antiferromagnetic order observed in Fig. 2c are occurring at ferroelectric domain walls. As a final experiment, a fully quantitative magnetic field image was recorded above the ferroelectic monodomain shown in Fig. 3a. Here the magnetic field component B NV was obtained by measuring the Zeeman shift ∆ z of the NV defect electron spin sublevels at each pixel of the scan [cf. Methods]. The resulting magnetic field map indicates a modulation with a typical amplitude in the range of ±140 µT [Fig. 4a]. In order to understand quantitatively such experimental data, we start by computing the stray field produced by the BFO sample. To this end, the spin cycloid is modeled by a rotating uncompensated magnetization vector M eff = m eff /V , where V is the volume of the pseudo-cubic cell of BFO and

Figure 4 : 4 |

 44 Figure 4: Figure 4 | Quantitative analysis of the spin cycloid magnetic texture. a, Fully quantitative magnetic field distribution B NV recorded above the ferroelectric monodomain shown in

- 2 )Fig. 2 ]

 22 Fig. 2], while the second one is rotated in plane by 90 • so that (001) B (001) D and [100] B [ 110] D [blue color in Extended Data Fig. 2]. We found β =89.2 • , α = γ =90 • , a = 0.5601 nm, b = 0.5572 nm and

  Fig. 4b. The probe-to-sample distance d is then extracted by fitting the experimental data following the

• λ = 5 .

 5 14 ± 0.10 • /nm, leading to α c = 2.04 ± 0.02 • between neighboring antiferromagnetically coupled Fe atoms, which are separated by a = 0.395 nm [see Fig. 1b]. The resulting uncompensated magnetic moment per Fe atom is given by m eff = m Fe sin(α c /2) = 0.073 ± 0.001 µ B . • The thickness of the BFO sample is extracted through X-ray diffraction (XRD) measurements [see Extended Data Fig. 1b]. The peak-to-peak spacing of Laue fringes indicates a sample thickness t = 32 ± 2 nm.

This equation includes a two-dimensional convolution defined asf (x, y) * g(x, y) = x ,y =+∞ x ,y =-∞ f (x , y ) g(xx , yy ) dx dy ,(8)

Acknowledgements We thank J. P. Tetienne and T. Hingant for experimental assistance at the early stage of the project. We are grateful to J. M. D. Coey for fruitful discussions. This research has been supported by the European Research Council (ERC-StG-2014, IMAGINE), the European Union Seventh Framework Program (FP7/2007-2013) under the project DIADEMS and by the French Agence Nationale de la Recherche (ANR) through project FERROMON.

Data availability. The data that support the findings of this study are available from the corresponding author upon reasonable request.

Author contributions I.G., W.A., L.J.M. and S.C. performed the NV magnetometry experiments; I.G., W.A., L.J.M. and V.J. analyzed the data and performed magnetic modeling with assistance from M.V.; K.G. and C.C. fabricated the BFO sample; V.G. and S.F. performed the structural analysis and the piezoresponse force microscopy experiments; P.A. and P.M. engineered diamond tips hosting single NV defects; I.G., W.A., V.G., S.F., M.B. and V.J. wrote the manuscripts. All authors contributed to the interpretation of the data and commented on the manuscript.

Competing Interests

The authors declare no competing financial interests.

Stray magnetic field produced by the spin cycloid. In this section, we calculate the stray magnetic field produced by the spin cycloid. The general methodology can be summarized as follows. The spin texture of the BFO sample is first modeled by a magnetization vector M describing a cycloid. The magnetic potential Φ produced by a single layer of the sample is then computed using Fourier methods and the resulting magnetic field B m is obtained by using the relation B m = -∇Φ. The total magnetic field B produced at a distance z above the sample is then calculated by summing up the contributions from all monolayers.

The resulting magnetic field distribution is finally projected along the NV defect axis in order to obtain an analytical formula for B N V , which can be used to fit the experimental data. The geometry used for the calculation is schematically depicted in Extended Data Fig. 5.

As introduced in the main text, we consider the uncompensated magnetic moments induced (i) by the pure spin cycloid m eff and (ii) by the spin density wave m DM [Fig. 4b]. The resulting spin texture of the BFO sample is modeled by a magnetization vector M = (m eff + m DM )/V , where

A rotation matrix was used to translate this magnetization into the laboratory frame of reference (x, y, z), in which the NV defect quantization axis is defined.

We start by computing the magnetic potential Φ(x, y, z) produced by a monolayer of the BFO sample, i.e.

with a unit cell thickness a = 0.395 nm. The magnetic potential is given by [START_REF] Mikuszeit | Magnetostatics and the rotational sense of cycloidal spin spirals[END_REF][START_REF] Blakely | Potential Theory in Gravity and Magnetic Applications[END_REF] Φ(x, y, z) =

x ,y =+∞

The total magnetic field B produced by the sample is obtained by summing the contribution of each monolayer

where N is the number of atomic layer of the BFO sample.

The above equation can be further simplified as

where

Here t = N a is the total thickness of the BFO sample.

This magnetic field distribution is finally projected along the NV defect axis in order to obtain an analytical formula for B NV , which is given

where (θ, φ) are the spherical angles of the NV axis in the laboratory frame.

Equation (17) was used to perform a two-dimensional fit of the experimental data, while using m DM as the only free parameter. The quality of the fit is illustrated by Extended Data Fig. 6b. magnetization M of the BFO sample was discretized into uniformly magnetized computation cells with a characteristic mesh volume 1 × 1 × 1 nm 3 . The magnetic field distribution produced by each magnetization cell was computed at a distance d above the sample surface using standard magnetostatic theory [START_REF] Rondin | Nanoscale magnetic field mapping with a single spin scanning probe magnetometer[END_REF] . By summing the contributions of all cells and then projecting along the NV defect quantization axis, we finally obtain a simulation of the stray field distribution B NV . Such a numerical simulation is in excellent agreement with the analytical calculation with a deviation smaller than 1%.

Effect of the cycloid chirality. In the previous sections, the calculation of the stray field above the BFO sample was performed for a spin cycloid with a counterclockwise (c-cw) chirality. It was emphasized in

Ref. 29 that the stray field depends on the chirality of the spin cycloid. By considering a clockwise (cw) chirality, the uncompensated magnetic moment induced by the spin cycloid is modified as

On the other hand, the magnetization distribution resulting from the SDW is independent of the chirality.

The resulting magnetic field distribution is then given by

where

The only difference between this magnetic field distribution and the one obtained for a counterclockwise chirality is the constant C


Keywords: diet, physical activity, sedentary behaviour, energy balance-related behaviours, lifestyle patterns, early childhood, tracking

Traditional approaches to understanding the behavioural determinants of adiposity have considered diet, physical activity and sedentary behaviour in isolation. Although integrative approaches have identified a variety of lifestyle patterns in children at preschool-age or older, along with some variability by socio-economic positions, this has rarely been examined in younger cohorts. We aimed to identify lifestyle patterns at 1.5, 3.5 and 5 years, including dietary intake, outdoor time and television viewing time, to assess associations with maternal education (as a proxy for socio-economic position), and to investigate their persistence between toddlerhood and preschool age. Participants were 417 and 293 children aged 1.5 y from the Melbourne Infant Feeding Activity and Nutrition Trial (InFANT) and InFANT Extend Programs, respectively. Data were collected using questionnaires at child ages 1.5, 3.5 and 5 y (InFANT); and 1.5 and 3.5 y (InFANT Extend). Principal component analysis was undertaken at each time point on the separate and pooled datasets. Associations between the lifestyle patterns scores and maternal education were assessed with multivariable regression analysis. Two lifestyle patterns ("Discretionary consumption and TV" and "Fruit, vegetables and outdoor") were identified as early as 1.5 y. They remained consistent across ages and were evident in both datasets. These patterns were inversely and positively associated with maternal education, respectively. Such early clustering of obesity related energy balance behaviours and tracking during early childhood suggests there may be shared antecedents common to the individual behaviours that could be targeted for intervention. Our findings provide support for interventions targeting multiple behaviours and tailored to the level of family socio-economic disadvantage.

Introduction

Childhood overweight and obesity is common from as early as two years of age and increases the probability of persistent unhealthy weight into adulthood [START_REF] Simmonds | Predicting adult obesity from childhood obesity: A systematic review and meta-analysis[END_REF][START_REF] Kim | Overweight or obesity in children aged 0 to 6 and the risk of adult metabolic syndrome: A systematic review and meta-analysis[END_REF], impairing both physical and mental health across the life-course [START_REF] Reilly | Long-term impact of overweight and obesity in childhood and adolescence on morbidity and premature mortality in adulthood: Systematic review[END_REF]. Beyond genetic or epigenetic susceptibilities, unhealthy lifestyle behaviours such as energy-dense, micronutrient-poor dietary intake, and high levels of screen time (mainly television viewing) are known to promote overweight and obesity [START_REF]Diet, Nutrition, and The Prevention of Chronic Diseases; Report of a joint WHO/FAO Expert Conultation[END_REF][START_REF] Swinburn | Diet, nutrition and the prevention of excess weight gain and obesity[END_REF]. In contrast, a healthier diet and physical activity are known to be protective [START_REF] Swinburn | Diet, nutrition and the prevention of excess weight gain and obesity[END_REF][START_REF] Te Velde | Energy balance-related behaviours associated with overweight and obesity in preschool children: A systematic review of prospective studies[END_REF].

Traditional approaches to understanding the determinants of adiposity have considered these lifestyle behaviours in isolation; however this approach fails to account for the known correlation or clustering of such behaviours in individuals [START_REF] Mcaloney | A scoping review of statistical approaches to the analysis of multiple health-related behaviours[END_REF]. Applying more integrative approaches based on pattern analyses, a number of studies conducted in children of preschool-age or older have identified a variety of patterns combining both healthy and unhealthy behaviours [START_REF] Gubbels | Physical Activity, Sedentary Behavior, and Dietary Patterns among Children[END_REF][START_REF] Leech | The clustering of diet, physical activity and sedentary behavior in children and adolescents: A review[END_REF]. The two most commonly observed lifestyle patterns in children are a "Snacking and sedentary" pattern, characterized by high consumption of energy-dense or processed foods along with high screen time (mostly television); and a "Healthy diet and physically active" pattern, often characterized by high consumption of core foods such as fruit and vegetables, along with high levels of physical activity. These two socio-economically differentiated lifestyle patterns are important as they reflect inter-related behavioural combinations that contribute either positively or negatively to energy balance, and have been shown to be associated with higher vs. lower risk of obesity in children [START_REF] Gubbels | Physical Activity, Sedentary Behavior, and Dietary Patterns among Children[END_REF][START_REF] Leech | The clustering of diet, physical activity and sedentary behavior in children and adolescents: A review[END_REF][START_REF] Magee | Patterns of health behaviours predict obesity in Australian children[END_REF][START_REF] Santaliestra-Pasias | Clustering of lifestyle behaviours and relation to body composition in European children. The IDEFICS study[END_REF][START_REF] Wadolowska | Prudent-Active and Fast-Food-Sedentary Dietary-Lifestyle Patterns: The Association with Adiposity, Nutrition Knowledge and Sociodemographic Factors in Polish Teenagers-The ABC of Healthy Eating Project[END_REF]. Analysing the socio-demographic characteristics of the population groups exposed to co-occurrence or clustering of unhealthy behaviours can also inform the targeting of obesity prevention interventions.

While there is evidence to suggest that dietary habits, physical activity and sedentary screen behaviour are established early and remain constant across childhood [START_REF] Jones | Tracking physical activity and sedentary behavior in childhood: A systematic review[END_REF][START_REF] Lioret | Dietary patterns track from infancy to preschool age: Cross-sectional and longitudinal perspectives[END_REF][START_REF] Luque | Unhealthy Dietary Patterns Established in Infancy Track to Mid-Childhood: The EU Childhood Obesity Project[END_REF] and into adulthood [START_REF] Mikkila | Consistent dietary patterns identified from childhood to adulthood: The cardiovascular risk in Young Finns Study[END_REF], to our knowledge, only one study (in two-year-olds) has been published on the clustering of lifestyle behaviours prior to preschool age [START_REF] Gubbels | Clustering of dietary intake and sedentary behavior in 2-year-old children[END_REF]. No study has assessed whether lifestyle patterns appear earlier than two years, nor their persistence throughout early childhood.

To address this gap, the objectives of the present study were to identify lifestyle patterns at 1.5, 3.5 and 5 years, including dietary intake, outdoor time and television viewing time, to assess their associations with maternal education (used as a proxy for socio-economic position), and to investigate the extent to which these patterns are stable from toddlerhood to preschool age.

Materials and Methods

Study Design and Participants

The Melbourne Infant Feeding Activity and Nutrition Trial (InFANT) and InFANT Extend Programs are separate cluster randomized controlled trials, which have been described in detail elsewhere [START_REF] Campbell | The Infant Feeding Activity and Nutrition Trial (INFANT) an early intervention to prevent childhood obesity: Cluster-randomised controlled trial[END_REF][START_REF] Hesketh | The Melbourne Infant Feeding, Activity and Nutrition Trial (InFANT) Program follow-up[END_REF][START_REF] Campbell | The extended Infant Feeding, Activity and Nutrition Trial (InFANT Extend) Program: A cluster-randomized controlled trial of an early intervention to prevent childhood obesity[END_REF]. For both interventions, eligibility involved being a first-time mother of an infant aged around 4 months of age and being able to communicate in English. Of those eligible, 86% (n = 542) and 97% (n = 514) consented to participate in the InFANT and InFANT Extend Programs, respectively. Given the similarity of studies and measures, we pooled data in order to increase power and therefore robustness of the current analyses.

The InFANT Program was a two arm cluster randomised controlled trial that commenced in 2008. Eligible mothers and their infants were recruited from 62 first-time parent groups organized by the universal Maternal and Child Health service provided across Victoria, Australia [START_REF] Campbell | The Infant Feeding Activity and Nutrition Trial (INFANT) an early intervention to prevent childhood obesity: Cluster-randomised controlled trial[END_REF][START_REF] Hesketh | The Melbourne Infant Feeding, Activity and Nutrition Trial (InFANT) Program follow-up[END_REF]. Families were randomised at the group level to the control or intervention condition. Parents in the intervention group were offered six 2-h dietitian delivered sessions over 15 months, focusing on parental knowledge, skills, and social support around infant feeding, diet, physical activity, and television viewing. The primary aim was to improve lifestyle behaviours and BMI z-scores. Measures were collected at baseline (mean age 4 months), end of intervention (mean age 20 months), and at follow-ups 2 and 3.5 years post intervention (child age approx. 3.5 and 5 y, respectively). Ethical approval was granted by Deakin University's Human Ethics Research Committee (EC175-2007) and the Victorian Office for Children (CDF/07/1138) and the trial was registered with the ISRCTN Register (ISRCTN81847050).

The Extended Infant Feeding, Activity and Nutrition Trial (InFANT Extend) employed similar methodology to the Melbourne InFANT Program [START_REF] Campbell | The extended Infant Feeding, Activity and Nutrition Trial (InFANT Extend) Program: A cluster-randomized controlled trial of an early intervention to prevent childhood obesity[END_REF]. This trial tested the efficacy of an extended (33 vs. 15

Measurements

Data used in the current study were collected using self-administered questionnaires provided to the main carer (mostly mothers). Eight variables describing usual dietary intake, outdoor time and television time, available at all relevant time points across both studies, i.e., 1.7, 3.5 and 5 y in InFANT and 1.6 and 3.2 y in InFANT Extend, were included in the pattern analyses. For the sake of simplicity, we refer to these three ages as 1.5 y, 3.5 y and 5 y throughout the manuscript, although due to scheduling of visits not all children were the exact age at measurement.

Dietary Intake

Usual dietary intake over the last month was assessed using a 66-item food frequency questionnaire (FFQ) (under review). Nine possible response categories ranged from 'never or less than once a month' to '6 or more times a day'. Portion sizes for each FFQ item were generated based on median portion sizes consumed at each age in the 2007 National Children's Nutrition and Physical Activity Survey data [START_REF]Australian Food Supplement and Nutrient Database[END_REF] and applied to each FFQ item. Daily consumption of each FFQ food item in grams was calculated by converting the frequency of consumption into daily equivalents (Never = 0; 1-3/month = 0.067; 1/week = 0.143; 2-4/week = 0.429; 5-6/week = 0.786; 1/day = 1.0; 2-3/day = 2.5; 4-5/day = 4.5; ≥6/day = 6.0 times per day) and then multiplying by the calculated median portion size for that food to generate grams per day (g/d). Consistent with the main dietary outcomes of the InFANT [START_REF] Campbell | The Infant Feeding Activity and Nutrition Trial (INFANT) an early intervention to prevent childhood obesity: Cluster-randomised controlled trial[END_REF][START_REF] Hesketh | The Melbourne Infant Feeding, Activity and Nutrition Trial (InFANT) Program follow-up[END_REF] and InFANT Extend [START_REF] Campbell | The extended Infant Feeding, Activity and Nutrition Trial (InFANT Extend) Program: A cluster-randomized controlled trial of an early intervention to prevent childhood obesity[END_REF] protocols, six food/drink groups were retained for inclusion in the current lifestyle pattern analysis, i.e., fruit, vegetables, water, sweet drinks, discretionary sweet foods, and discretionary savory foods (all measured in g/d). There was a ceiling effect for water intake, as about half of parents reported their child consumed six or more serves/d (converted to 1050 g/d). This variable was therefore dichotomized as consuming ≥1050 g/d of water vs. <1050 g/d at each of the time points. Likewise, sweet drinks were consumed by <50% of the children at 1.5 y in both InFANT and InFANT Extend, and were dichotomized into consumers vs. non-consumers at this age. Because we used a pattern analysis sensitive to outliers (see Statistical Analyses section), values for outliers were replaced by the maximum values of the remaining distributions at each age in the InFANT and InFANT Extend samples (n = 17 and 12 respectively).

Outdoor Time

Parents reported the number of minutes (open response) their child spent outside on a typical day. Parent-reported usual outdoor time has been shown to be associated with direct objective measurement of physical activity by accelerometer in preschool-aged children [START_REF] Burdette | Parental report of outdoor playtime as a measure of physical activity in preschool-aged children[END_REF]. Values for outliers were replaced by the maximum values of the remaining distributions at each age in InFANT and InFANT Extend samples (n = 2 and 3 respectively).

Television Viewing Time

Parents reported the number of minutes (open response) their child spent watching or in front of the television on a typical day using items with established reliability [START_REF] Hinkley | The HAPPY study: Development and reliability of a parent survey to assess correlates of preschool children's physical activity[END_REF]. Test-retest reliability in this sample indicated good convergence with intraclass correlation coefficient ICC = 0.69 at 3 months of age and ICC > 0.79 for other ages. Values for outliers were replaced by the maximum value of the remaining distributions at each age in InFANT and InFANT Extend (n = 2 and 3 respectively).

Demographic, Socioeconomic and Anthropometric Factors

Demographic, socioeconomic and anthropometric data reported at baseline included children's sex and birth weight and mother's country of birth and maternal education level. The latter was defined in three categories: low (secondary school or below), intermediate (trade and certification qualifications) and high (university degree). Maternal education is the indicator most commonly used as a proxy for socio-economic position when considering lifestyle behaviours of children [START_REF] Ensminger | A decade of measuring SES: What it tells us and where to go from here[END_REF]; also, it is consistently and strongly associated with child adiposity in the literature [START_REF] Shrewsbury | Socioeconomic Status and Adiposity in Childhood: A Systematic Review of Cross-sectional Studies 1990-2005[END_REF] and is less likely to be affected by motherhood, as compared to other indicators such as income and occupation.

Included Samples

Of the 542 and 514 mother-child dyads initially recruited to InFANT and InFANT Extend, respectively, 179 and 168 participants dropped out between enrolment and the end of follow-up, i.e., at 5 y in InFANT and at 3.5 y in InFANT Extend ( Figure 1; Figure 2). Additionally, children with missing information on any of the behaviours of interest for the current study were excluded from the analysis (n = 75 at 1.5 y; n = 73 at 3.5 y; and n = 58 at 5 y for InFANT; n = 109 at 1.5 y; and n = 72 at 3.5 y for InFANT Extend), resulting in 417, 297 and 305 eligible children for analysis at 1.5, 3.5 and 5 y in InFANT; and 293 and 274 at 1.5 and 3.5 y in InFANT Extend. We derived lifestyle patterns for all subjects with complete data at each age. Multi-time-point lifestyle patterns were also assessed in the 247 and 210 children with data available at all three ages in InFANT and at the two ages in InFANT Extend, respectively.

Statistical Analyses

We described the children from the InFANT (n = 417) and InFANT Extend (n = 293) datasets who had all behavioural data available at approx. 1.5 y. Socio-demographic and anthropometric factors were then compared between this sample and the children assessed at baseline (children aged 4 months) but not included in the analysis undertaken at 1.5 y, because of loss to follow-up or missing data (n = 125 and n = 221, respectively). Chi-square and Student t tests were used to compare frequencies and means, respectively.

Different data-driven approaches have been used to identify both dietary and lifestyle patterns, in particular principal component analysis (PCA) and cluster analysis (CA). These approaches have shown good reproducibility [START_REF] Gubbels | Physical Activity, Sedentary Behavior, and Dietary Patterns among Children[END_REF][START_REF] Leech | The clustering of diet, physical activity and sedentary behavior in children and adolescents: A review[END_REF][START_REF] Newby | Empirically derived eating patterns using factor or cluster analysis: A review[END_REF]. PCA allows the synthesis of a large number of supposedly correlated variables into a fewer number of patterns, which are linear combinations of the initial standardized variables: each subject from the analytical sample has a score on each of the patterns derived. CA reduces data into mutually exclusive groups (clusters) based upon individual differences in mean intakes: subjects are member of one given cluster. In the current analysis, we aimed to measure adherence to each of the patterns derived, and not separate children in mutually exclusive groups, which led us to use PCA.

Cross-sectional lifestyle patterns were first derived independently at 1.5 y and 3.5 y (InFANT and InFANT Extend) and 5 y (InFANT) using PCA with varimax rotation of the 8 standardized behavioural variables, i.e., fruit, vegetables, water, sweet drinks, discretionary sweet foods, discretionary savory foods, outdoor and television viewing time. The number of patterns was selected considering eigenvalues >1.0, the scree plot and the interpretability of the patterns [START_REF] Cattell | The scree test for the number of factors[END_REF][START_REF] Kline | An Easy Guide to Factor Analysis[END_REF]. To interpret and label each pattern, we considered the items most strongly related to that pattern, i.e., those for which the absolute value of the loading coefficient (i.e., the correlation of each variable with the given lifestyle pattern) was >0.25. The PCA scores for each lifestyle pattern were calculated at the individual level by summing the observed standardized values of each variable, weighted according to the PCA loadings.

Longitudinal, multi-time-point lifestyle patterns were then derived in a separate PCA with varimax rotation, for each study, including simultaneously the standardized variables defined at all available time points, i.e., 1.5 y, 3 y and 5 y (InFANT, n = 247); and 1.5 y and 3 y (InFANT Extend, n = 210). The same criteria were considered to retain and label the resulting patterns. This longitudinal application of PCA was previously used by Brazionis et al. [START_REF] Brazionis | Characterization of transition diets spanning infancy and toddlerhood: A novel, multiple-time-point application of principal components analysis[END_REF] to assess transition diets in the early years and by Lioret et al. [START_REF] Lioret | Dietary patterns track from infancy to preschool age: Cross-sectional and longitudinal perspectives[END_REF] as a longitudinal measure of tracking on dietary patterns. Persistence of patterns from 1.5 y to 5 y (InFANT, n = 247) and from 1.5 y to 3.5 y (InFANT Extend, n = 210) was also assessed with Pearson correlation coefficients and associated p-values estimated between lifestyle patterns in each dataset. Recommendations for interpreting these correlation coefficients are: low 0.1-0.3, medium 0.3-0.5 and high >0.5 [START_REF] Cohen | Statistical Power Analysis for the Behavioural Science[END_REF]. Sensitivity pattern analyses were undertaken on the pooled InFANT and InFANT Extend datasets at 1.5 y (n = 710) and 3.5 y (n = 571). Of note, consistent loading coefficients were observed from PCA independently undertaken in intervention and control groups (results available on request); findings from the whole InFANT and InFANT Extend samples were, however, prioritized to allow a higher statistical power and therefore precision of the estimated scores. Lastly, we performed multivariable linear regression analysis to investigate the relations between a given lifestyle pattern (as the outcome) and maternal education level, adjusting for child sex, age, treatment and using the survey command in Stata (to account for clustering by first-time parent group). This analysis was performed in each of the pooled 1.5 y and 3.5 y samples to avoid multiple comparisons. Adjusted parameter estimates and 95% CIs were calculated.

Results

Characteristics of the Study Population

Children were aged on average 1.6 (SD = 0.2), 3.6 (0.2), and 5.0 (0.1) y at the three time points in InFANT; and 1.6 (0.1) and 3.2 (0.1) y at the two time points in InFANT Extend. Sample characteristics are presented in Table 1. In InFANT Extend, the 221 children excluded from the analyses at 1.5 y due to loss at follow-up or missing data came from families where the mothers were younger and less likely to have achieved a high education level compared to those retained in the analyses; there were no such differences in InFANT.

Characteristics of Lifestyle Patterns

Cross-Sectional PCA Approach Two consistent lifestyle patterns were identified in each of the independent analyses across time points and study populations. Each of these patterns accounted for 18.3-22.0% of the explained variance (Table 2). Overall, at each time point, one pattern was consistently and positively correlated with intakes of sweet drinks, discretionary sweet foods, discretionary savory foods and television time. We labelled this pattern "Discretionary consumption and TV" (referred to as LP1 in the tables). The other pattern, labelled "Fruit, vegetables and outdoor" (referred to as LP2 in the tables), was mainly characterized by high intake of fruit and vegetables and high levels of outdoor time. When the absolute value of water intake loaded 0.25, water was either negatively correlated with the "Discretionary consumption and TV" pattern, or positively correlated with the "Fruit, vegetables and outdoor" pattern. Consistent findings were obtained from analyses using the pooled InFANT-InFANT Extend dataset at 1.5 and 3.5 y (Table 3). a Values are % yes (water intake; and sweet drinks intake at 1.5 years) or mean (SD); b LP1: "Discretionary consumption and TV" lifestyle pattern; c LP2: "Fruit, vegetables and outdoor" lifestyle pattern. d Fruit was summed consumption of 10 fruits; at 1.5 y in the InFANT sample banana was not reported so fruit was summed consumption of nine fruits. In bold: Factor loadings <-0.25 or >0.25. In bold: Factor loadings <-0.25 or >0.25.

Persistence of Lifestyle Patterns from Toddlerhood to Preschool Age

Longitudinal PCA Approach

Consistent with the findings in the cross-sectional approach, in longitudinal analyses, we identified the two multi-time-point lifestyle patterns, "Discretionary consumption and TV" and "Fruit, vegetables and outdoor", spanning 1.5 to 5 y in InFANT and 1.5 to 3.5 y in InFANT Extend. These accounted for 13.2-16.4% of the explained variance (Supplementary Materials Table S1).

Correlation Approach

Correlation coefficients between the "Discretionary consumption and TV" pattern observed at 1.5 y, 3.5 y and 5 y respectively were universally high (0.50-0.63) [START_REF] Cohen | Statistical Power Analysis for the Behavioural Science[END_REF], with corresponding coefficients for the "Fruit, vegetables and outdoor" pattern at different ages being medium to high (0.36-0.60) (Table 4).

Associations with Maternal Education

The "Discretionary consumption and TV" pattern was inversely associated with maternal education level at both 1.5 (significant trend) and 3.5 y in the pooled datasets (Table 5). Conversely, the "Fruit, vegetables and outdoor" pattern was positively associated with maternal education at 1.5 y.

Discussion

To the best of our knowledge, this study is the first to show that lifestyle patterns, namely "Discretionary consumption and TV" and "Fruit, vegetables and outdoor", are established by 1.5 years of age. Further, there is evidence of persistence of these lifestyle patterns across early childhood, and that these patterns are influenced by maternal education.

Similar patterns to those identified in this study have been reported in other studies of early childhood populations. In the study most comparable to ours, using PCA, Gubbels et al. [START_REF] Gubbels | Clustering of dietary intake and sedentary behavior in 2-year-old children[END_REF] found a "Snacking-sedentary" pattern in toddlers aged 2 y in the Netherlands, which was characterized by eating snacks, drinking sugar-sweetened beverages, television viewing and computer use. Lifestyle patterns characterized by less healthy foods and drinks, and screen time, have also been described using either PCA or cluster analysis in children aged 3-6 years across Europe [START_REF] Lioret | Dietary and physical activity patterns in French children are related to overweight and socioeconomic status[END_REF][START_REF] Gubbels | Energy balance-related behavioural patterns in 5-year-old children and the longitudinal association with weight status development in early childhood[END_REF][START_REF] Miguel-Berges | Clustering of energy balance-related behaviours and parental education in European preschool children: The ToyBox study[END_REF]. This consistency across countries, datasets and methods used to derive such patterns has also been confirmed in school-aged children [START_REF] Gubbels | Physical Activity, Sedentary Behavior, and Dietary Patterns among Children[END_REF][START_REF] Leech | The clustering of diet, physical activity and sedentary behavior in children and adolescents: A review[END_REF][START_REF] Magee | Patterns of health behaviours predict obesity in Australian children[END_REF][START_REF] Leech | Clustering of children's obesity-related behaviours: Associations with sociodemographic indicators[END_REF][START_REF] Leech | Clustering of diet, physical activity and sedentary behaviour among Australian children: Cross-sectional and longitudinal associations with overweight and obesity[END_REF][START_REF] Bel-Serrat | Clustering of Multiple Energy Balance-Related Behaviors in School Children and its Association with Overweight and Obesity-WHO European Childhood Obesity Surveillance Initiative (COSI 2015(-)2017)[END_REF]. Consistent with our findings, these lifestyle patterns were typically inversely associated with parental socio-economic positions in other studies, most commonly approximated by maternal education [START_REF] Gubbels | Physical Activity, Sedentary Behavior, and Dietary Patterns among Children[END_REF][START_REF] Leech | The clustering of diet, physical activity and sedentary behavior in children and adolescents: A review[END_REF][START_REF] Leech | Clustering of diet, physical activity and sedentary behaviour among Australian children: Cross-sectional and longitudinal associations with overweight and obesity[END_REF]. The co-occurrence between television viewing and unhealthy dietary habits has often been described in the literature. Proposed mechanisms include: watching TV or movies as a hand-free passive occupation enables snacking; exposure to advertising of junk food and fast food when watching TV may increase children's requests for those particular foods and products; and viewing screens while eating distracts from internal satiety cues potentially leading to overconsumption [START_REF] Temple | Television watching increases motivated responding for food and energy intake in children[END_REF][START_REF] Rey-Lopez | Sedentary behaviour and obesity development in children and adolescents[END_REF][START_REF] Dalton | Child-targeted fast-food television advertising exposure is linked with fast-food intake among pre-school children[END_REF]. Notably, a lifestyle pattern characterized by consumption of discretionary foods and drinks, and elevated screen time, is the pattern most often associated with child overweight in the literature [START_REF] Gubbels | Physical Activity, Sedentary Behavior, and Dietary Patterns among Children[END_REF][START_REF] Leech | The clustering of diet, physical activity and sedentary behavior in children and adolescents: A review[END_REF][START_REF] Magee | Patterns of health behaviours predict obesity in Australian children[END_REF][START_REF] Santaliestra-Pasias | Clustering of lifestyle behaviours and relation to body composition in European children. The IDEFICS study[END_REF][START_REF] Wadolowska | Prudent-Active and Fast-Food-Sedentary Dietary-Lifestyle Patterns: The Association with Adiposity, Nutrition Knowledge and Sociodemographic Factors in Polish Teenagers-The ABC of Healthy Eating Project[END_REF][START_REF] Leech | Clustering of diet, physical activity and sedentary behaviour among Australian children: Cross-sectional and longitudinal associations with overweight and obesity[END_REF][START_REF] Bel-Serrat | Clustering of Multiple Energy Balance-Related Behaviors in School Children and its Association with Overweight and Obesity-WHO European Childhood Obesity Surveillance Initiative (COSI 2015(-)2017)[END_REF].

The lifestyle pattern characterized by the high consumption of core foods such as fruit and vegetables, along with increased time spent in physical activities (referred to here as "Fruit, vegetables and outdoor") has been less frequently identified in other studies, and only in children aged 3 y or older [START_REF] Gubbels | Physical Activity, Sedentary Behavior, and Dietary Patterns among Children[END_REF][START_REF] Leech | The clustering of diet, physical activity and sedentary behavior in children and adolescents: A review[END_REF][START_REF] Magee | Patterns of health behaviours predict obesity in Australian children[END_REF][START_REF] Bel-Serrat | Clustering of Multiple Energy Balance-Related Behaviors in School Children and its Association with Overweight and Obesity-WHO European Childhood Obesity Surveillance Initiative (COSI 2015(-)2017)[END_REF]. Among pre-schoolers, Lioret et al. [START_REF] Lioret | Dietary and physical activity patterns in French children are related to overweight and socioeconomic status[END_REF] identified a "Varied food and physically active" pattern in 3-6 y French children; and Miguel-Berges et al. [START_REF] Miguel-Berges | Clustering of energy balance-related behaviours and parental education in European preschool children: The ToyBox study[END_REF] identified a "Healthy lifestyle" pattern in European preschool-aged children (3.5-5.5 y), characterized not only by high water, fruit, vegetable intake and sports participation, but also by increased sleep time; and reduced soft drinks and screen time. A very similar healthy pattern was described in Australian children aged 6-7 y [START_REF] Magee | Patterns of health behaviours predict obesity in Australian children[END_REF]. This lifestyle pattern, combining a range of healthy behaviours, has most often been found to be positively associated with parental socio-economic position (often approximated by maternal education) [START_REF] Gubbels | Physical Activity, Sedentary Behavior, and Dietary Patterns among Children[END_REF][START_REF] Leech | The clustering of diet, physical activity and sedentary behavior in children and adolescents: A review[END_REF][START_REF] Magee | Patterns of health behaviours predict obesity in Australian children[END_REF], which our findings confirm at 1.5 y. This socioeconomic disparity may reflect varying family knowledge, social norms, attitudes, and lifestyles, within an environment providing differential access to both healthy food and safe places to play outside. It is important to note that young children are mostly controlled and influenced by their parents, who are also usually their main role models and providers [START_REF] Golan | Parents are key players in the prevention and treatment of weight-related problems[END_REF]. There is some evidence to suggest that children's lifestyle, whether diet, physical activity or sedentary behaviours, is strongly associated with their parents' diet and physical activity, and with parent capacity to control the availability of healthy foods at home and engage their children in physical activities [START_REF] Cleland | Predictors of time spent outdoors among children: 5-year longitudinal findings[END_REF][START_REF] Rodenburg | Clustering of food and activity preferences in primary school children[END_REF][START_REF] Lioret | Association between maternal education and diet of children at 9 months is partially explained by mothers' diet[END_REF]. Potentially, the same parents who are aware of, value, and have the resources to provide a healthy diet, will also be aware of, value and have the resources to promote physical activity and limit screen time, leading to an "overall healthy" lifestyle pattern.

Tracking from early life of each of the lifestyle behaviours under study has been previously described [START_REF] Jones | Tracking physical activity and sedentary behavior in childhood: A systematic review[END_REF][START_REF] Lioret | Dietary patterns track from infancy to preschool age: Cross-sectional and longitudinal perspectives[END_REF][START_REF] Luque | Unhealthy Dietary Patterns Established in Infancy Track to Mid-Childhood: The EU Childhood Obesity Project[END_REF]. The present study, however, further highlights that combinations of either healthy or unhealthy behaviours persist from as early as 1.5 y, which provides new and important insights into the genesis of these behaviours. Not only have we shown that similar lifestyle patterns were overall highly correlated between 1.5, 3.5 and 5 y in InFANT, especially for unhealthy behaviours, but we have also derived two longitudinal multi-time point patterns, each characterized by repeated exposures to the same behaviours over time. Higher scores for "Discretionary consumption and TV at 1.5, 3.5 and 5 y" reflect higher tracking for this particular pattern of behaviours, whereas higher scores for the "Fruit, vegetables and outdoor at 1.5, 3.5 and 5 y" pattern may be interpreted as a stable adherence to a healthy lifestyle across early childhood. Consistent findings and interpretations from both InFANT and InFANT Extend datasets suggests robustness of these patterns across samples. Another study examining the clustering of energy balance-related behaviours in a smaller sample of Australian school-aged children (123 aged 5-6 and 87 children aged 10-12 y at baseline) found fair to moderate persistence of lifestyle cluster membership over three years, providing further evidence for the early establishment of clusters of obesogenic lifestyle behaviours [START_REF] Leech | Clustering of diet, physical activity and sedentary behaviour among Australian children: Cross-sectional and longitudinal associations with overweight and obesity[END_REF]. In that study, the clusters of obesity-promoting behaviours were hypothesized to lead to cumulative increases in positive energy balance over the life course.

These findings have important implications for conceptualizing early obesity prevention policy and practice. A better understanding of when, which and in whom behaviours co-occur and start to track collectively over time informs the design and delivery of interventions targeting groups of behaviours rather than individual behaviours. Importantly, these findings will also inform policy that guides provision of early childhood care, ensuring that the large numbers of children in childcare are supported to achieve healthy behavioural patterns. It has also been hypothesized that with behaviours that co-occur, change in one may support change in the other, highlighting the potential for multiple-behaviour interventions to have a greater impact on public health than single-behaviour interventions, especially for preventing multifactorial health conditions [START_REF] Prochaska | Multiple health behavior change research: An introduction and overview[END_REF][START_REF] Prochaska | Multiple Health Behavior Research represents the future of preventive medicine[END_REF]. Interventions focusing on reducing television time, along with the promotion of physical activity engagement and healthy eating, therefore may be promising, especially in children of less educated mothers. Such integrated interventions may have the potential to provide a synergistic impact on health behaviours that goes beyond the simple additive effects of focusing on individual behaviours consecutively. This may help explain the greater success of multi-component interventions in the prevention of childhood overweight [START_REF] Prochaska | Multiple health behavior change research: An introduction and overview[END_REF][START_REF] Prochaska | Multiple Health Behavior Research represents the future of preventive medicine[END_REF].

Limitations and Strengths

In interpreting the findings of the present study, it is important to acknowledge several limitations. Parental self-report of children's behaviours is subject to measurement error, i.e., social desirability bias and relative imprecision as compared to objective measurements (e.g., using accelerometry for physical activity). With respect to food intake, frequency of consumption has been shown to be the major determinant of dietary intake [START_REF] Noethlings | Portion size adds limited information on variance in food intake of participants in the EPIC-Potsdam study[END_REF]. The FFQ used across the studies was developed specifically for this age group and has been validated against three 24 h recalls in children aged 1.5, 3.5 and 5.0 y: fair agreement for most nutrient and food intakes was observed, with acceptable rankings of intake suitable for use in PCA (which is based on the underlying correlation matrix) (under review). Additionally, outdoor time has been positively associated with objectively-measured PA in pre-schoolers [START_REF] Burdette | Parental report of outdoor playtime as a measure of physical activity in preschool-aged children[END_REF], and both outdoor and television viewing time have been found to be prospectively related to adiposity in early childhood [START_REF] Te Velde | Energy balance-related behaviours associated with overweight and obesity in preschool children: A systematic review of prospective studies[END_REF][START_REF] Saldanha-Gomes | Prospective associations between energy balance-related behaviors at 2 years of age and subsequent adiposity: The EDEN mother-child cohort[END_REF]. Of note, whereas accelerometry does provide objective information on duration and intensity of activities, the measurements of physical activity and sedentary screen behaviours used in the present study provide information on the context in which they take place (i.e., outdoor and television viewing), which is potentially useful for designing prevention interventions. The present study involved PCA, which is an exploratory statistical alternative among pattern analyses. Strict comparison with other findings is not straightforward due to the data driven approach to pattern analysis, with different methodologies employed in the collection of behavioural data, subjective redistribution of the former items (e.g., foods) into the variables used (e.g., food groups), the transformation of these variables (e.g., standardisation), the methods of rotation of components (if any) employed, and the number of patterns identified-all complicating the opportunities for comparison. Despite these potential variations in methodology, various reviews [START_REF] Gubbels | Physical Activity, Sedentary Behavior, and Dietary Patterns among Children[END_REF][START_REF] Leech | The clustering of diet, physical activity and sedentary behavior in children and adolescents: A review[END_REF][START_REF] Newby | Empirically derived eating patterns using factor or cluster analysis: A review[END_REF] have reported fairly good reproducibility between most studies which have identified either dietary or lifestyle patterns. This consistency and therefore robustness was confirmed in the present study. Regarding representativeness, although all levels of maternal education were represented in this study, the sample is generally well educated, with a majority having tertiary education. In addition, mothers excluded from the analyses tended to be less educated and younger, which is a common trait of cohort studies. Whereas these characteristics may have implications for generalizability, the lifestyle patterns derived here are rather consistent with other studies, both cross-sectional and longitudinal, performed in preschool and school-aged children in Australia and overseas.

Particular strengths of the study include consistent measures for a variety of behaviours across studies and time-points, relatively large sample sizes (particularly for pooled analyses), the longitudinal design, and the integrative approach of health behaviours.

Conclusion

In conclusion, healthy ("Fruit, vegetables and outdoor") and unhealthy ("Discretionary consumption and TV") lifestyle patterns were identified in the present study. These patterns were evident as early as 1.5 y of age, and were extremely robust-across samples and at different child ages. Similar patterns have been observed in a number of other studies carried out in older children [START_REF] Mcaloney | A scoping review of statistical approaches to the analysis of multiple health-related behaviours[END_REF][START_REF] Gubbels | Physical Activity, Sedentary Behavior, and Dietary Patterns among Children[END_REF][START_REF] Leech | The clustering of diet, physical activity and sedentary behavior in children and adolescents: A review[END_REF][START_REF] Brazionis | Characterization of transition diets spanning infancy and toddlerhood: A novel, multiple-time-point application of principal components analysis[END_REF][START_REF] Cohen | Statistical Power Analysis for the Behavioural Science[END_REF][START_REF] Lioret | Dietary and physical activity patterns in French children are related to overweight and socioeconomic status[END_REF][START_REF] Gubbels | Energy balance-related behavioural patterns in 5-year-old children and the longitudinal association with weight status development in early childhood[END_REF]. Such early clustering and tracking of healthy and unhealthy energy balance-related behaviours suggest there may be shared antecedents common to the individual behaviours that could be targeted for intervention. Finally, the association with maternal education level indicates that such multiple behaviour interventions may be more effective to prevent child overweight if adapted to the level of family social disadvantage.

Supplementary Materials:

The following are available online at http://www.mdpi.com/2072-6643/12/3/724/s1. Table S1: PCA loadings for the multi-time-point lifestyle patterns (LP) in InFANT from 1.5 y to 5 y and in InFANT Extend from 1.5 y to 3.5 y.

Author Contributions: S.L. conceptualized the study, conducted the analyses, and drafted the initial manuscript; K.J.C. and K.D.H. conceptualized and led the Infant and Infant Extend Studies; K.J.C. and K.D.H. contributed to the conceptualization of the current study and the analytic approach, contributed to the interpretation of results, drafted and edited the manuscript; G.A. guided the statistical analysis, conducted some of the analyses, contributed to the interpretation of results, drafted and edited the manuscript; K.J.C. and S.A.M. conducted the dietary data collection; S.A.M., A.J.C., K.J.C., K.D.H. and J.S. contributed to the interpretation of results, drafted and edited the manuscript. All authors approved the final manuscript as submitted and agree to be accountable for all aspects of the work. All authors have read and agreed to the published version of the manuscript.

Lifestyle

  Patterns Begin in Early Childhood, Persist and Are Socioeconomically Patterned, Confirming the Importance of Early Life Interventions Sandrine Lioret 1, *, Karen J. Campbell 2 , Sarah A. McNaughton 2 , Adrian J. Cameron 3 , Jo Salmon 2 , Gavin Abbott 2 and Kylie D. Hesketh 2

Figure 1 .

 1 Figure 1. Flow of participants through the Melbourne InFANT Program.

Figure 2 .

 2 Figure 2. Flow of participants through the Melbourne InFANT Extend Program.

  month) and enhanced (use of web-based materials, and Facebook ® engagement), version of the original Melbourne InFANT Program intervention in a new cohort of 514 families from 62 first-time parent groups in Melbourne, Australia, from 2010. Measures were collected at baseline (mean age 4 months), mid-intervention (mean age 19 months), and at intervention conclusion (mean age 38 months). Ethical approval was granted by Deakin (EC-175-2007 (Part 2-2007-175) and the Department of Education and Early Childhood Development (Victoria, Australia) (2011_001000) and was registered with ACTRN (ACTRN12611000386932).

Table 1 .

 1 Characteristics of the study samples.

	InFANT

Table 2 .

 2 Behavioural variables distribution and PCA loadings for lifestyle patterns (LP) derived at 1.5 y, 3.5 y and 5 y.

	Age	1.5 y

Table 3 .

 3 PCA loadings for lifestyle patterns (LP) derived at 1.5 y and 3.5 y in the pooled datasets (InFANT and InFANT Extend studies combined).

	Age	1.5 y		3.5 y
	n	710		571
	Behavioural variables	LP1	LP2	LP1	LP2
	Fruit	0.03	0.62	0.04	0.67
	Vegetables	-0.04	0.58	-0.06	0.64
	Water	-0.21	0.12	-0.24	0.15
	Sweet drinks	0.51	0.07	0.47	0.03
	Discretionary sweet foods	0.56	-0.04	0.49	0.02
	Discretionary savory foods	0.51	0.06	0.48	0.02
	TV	0.30	-0.27	0.46	-0.07
	Outdoor	0.15	0.43	0.15	0.33
	% variance explained	19.6	19.1	21.7	18.0
	Label	Discretionary consumption and TV	Fruit, vegetables and outdoor	Discretionary consumption and TV	Fruit, vegetables and outdoor

Table 4 .

 4 Pearson correlation coefficients1 and p-values between lifestyle patterns (LP) scores identified at 1.5 y, 3.5 y and 5 y.

	Study (n)	Age	3.5 y	5 y
			LP1	LP2	LP1	LP2
	InFANT (247)	1.5 y 3.5 y	LP1 0.52 *** -0.20 ** LP2 -0.05 0.47 *** LP1 LP2	0.50 *** -0.12 0.63 *** -0.23 *** 0.60 *** -0.17 ** 0.36 *** -0.13 *
	InFANT Extend (210) 1.5 y	LP1 0.51 *** LP2 -0.04	-0.06 0.51 ***
	* p < 0.05, ** p < 0.01, *** p < 0.001, n = 989; 1 Recommendations for interpreting these correlation coefficients: low
	<0.3, moderate 0.3-0.6 and high >0.6 [30]; LP1: "Discretionary consumption and TV" lifestyle pattern; LP2: "Fruit,
	vegetables and outdoor" lifestyle pattern.

Table 5 .

 5 Lifestyle pattern scores in the pooled InFANT and InFANT Extend datasets according to maternal education level (Adjusted a β parameter estimates and 95% confidence intervals).

	Lifestyle Pattern			LP1				LP2
	Age		1.5 y		3.5 y		1.5 y		3.5 y
		β	95% CI	β	95% CI	β	95% CI	β	95% CI
	n	708		567		708		567
	Maternal
	education
	Low	Ref		Ref		Ref		Ref
	Intermediate	0.01	-0.29; 0.31	-0.34	-0.77; 0.08	0.18	-0.12; 0.49	-0.15	-0.51; 0.20
	High	-0.22	-0.50; 0.05	-0.65	-0.98; -0.32	0.34	0.08; 0.59	-0.01	-0.33; 0.32
	p value	0.06		0.0002		0.03		0.45
	p trend	0.037		0.000		0.009

a Multivariable linear regression analyses accounted for child sex, age, treatment and clustering by first-time parent group. LP1: "Discretionary consumption and TV" lifestyle pattern; LP2: "Fruit, vegetables and outdoor" lifestyle pattern.

Funding: The Melbourne InFANT Program follow-ups were funded by a National Health and Medical Research Council Project Grant (APP1008879); the InFANT Extend Program was funded by a World Cancer Research Fund grant (no. 2010/244). SL was supported by an Alfred Deakin Postdoctoral fellowship (Deakin University, 2010-2012), a sabbatical at IPAN in 2018 funded by INSERM and The French National Research Agency grant (ANR-19-CE36-0006). AJC is the recipient of an Australian Research Council Discovery Early Career Researcher Awards (project number DE160100141). SAM is supported by an NHMRC Career Development Fellowship Level 2 (ID1104636). JS was supported by a National Health and Medical Research Council Principal Research Fellowship during this study (APP1026216). KDH is supported by an Australian Research Council Future Fellowship (FT130100637) and an Honorary Heart Foundation of Australia Future Leader Fellowship (100370).

Conflicts of Interest:

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.