Antiferromagnetic textures in BiFeO3 controlled by strain and electric field

Antiferromagnetic thin films are currently generating considerable excitement for low dissipation magnonics and spintronics. However, while tuneable antiferromagnetic textures form the backbone of functional devices, they are virtually unknown at the submicron scale. Here we image a wide variety of antiferromagnetic spin textures in multiferroic BiFeO3 thin films that can be tuned by strain and manipulated by electric fields through room-temperature magnetoelectric coupling. Using piezoresponse force microscopy and scanning NV magnetometry in self-organized ferroelectric patterns of BiFeO3, we reveal how strain stabilizes different types of non-collinear antiferromagnetic states (bulk-like and exotic spin cycloids) as well as collinear antiferromagnetic textures. Beyond these local-scale observations, resonant elastic X-ray scattering confirms the existence of both types of spin cycloids. Finally, we show that electric-field control of the ferroelectric landscape induces transitions either between collinear and non-collinear states or between different cycloids, offering perspectives for the design of reconfigurable antiferromagnetic spin textures on demand.

I n ferromagnetic materials, spin textures are conventionally tweaked with a magnetic field. Antiferromagnetic spin textures, on the other hand, are intrinsically insensitive to external magnetic fields, calling for alternative control knobs to manipulate the antiferromagnetic order. The electrical manipulation of antiferromagnetism was recently demonstrated in noncentrosymmetric metallic antiferromagnets [1][2][3] ; however, the spin orbit torque required to either switch by 90°or reverse by 180°t he antiferromagnetic vector involves large current densities of the order of 10 6 -10 7 A cm −2 . Furthermore, the efficiency of this writing method faces limitations, since only a small fraction of antiferromagnetic domains is actually switched 4,5 . An optimal writing mechanism would demand low current densities (or ideally no current) to generate a complete reversal of antiferromagnetic domains or textures. Recent reports have for instance demonstrated that piezoelectric strain can provide low power control of antiferromagnetic memories 6,7 .
In some materials possessing both antiferromagnetic and electrical orders, the magnetoelectric coupling is an additional means expected to efficiently channel electric-field stimuli onto the antiferromagnetic order. Yet, the fundamental ingredients deterministically governing the imprint of the ferroelectric order to the antiferromagnetic order remain poorly understood. Even in the archetypal room-temperature multiferroic 8 , BiFeO 3 , the details of the antiferromagnetic textures are virtually unknown at the scale of ferroelectric domains. The seminal work of Zhao et al. showed promise for the electric control of the antiferromagnetic order in BiFeO 3 thin films 9 . To date, its complex antiferromagnetic order has been solely inferred from volume averaged techniques such as neutron diffraction, Mössbauer spectroscopy, or Raman spectroscopy. Depending on the strain, growth conditions and crystal orientation, the magnetic state of BiFeO 3 thin films can either show different types of non-collinear cycloids, canted G-type antiferromagnetic orders, or even a mixture of these 10,11 . More generally, examples of antiferromagnetic textures being imaged at the nanoscale are extremely scarce in the literature [12][13][14] . Here we bring deep insight into the strain-dependent interplay between the ferroelectric and antiferromagnetic orders at the local scale and show that electric field can be used to convert between various collinear and noncollinear spin arrangements.

Results
Strain-engineered BiFeO 3 with striped ferroelectric domains. BiFeO 3 thin films were grown using pulsed laser deposition on various substrates (SrTiO 3 , DyScO 3 , TbScO 3 , GdScO 3 , SmScO 3 ) with a thin bottom electrode of SrRuO 3 (Methods). X-ray diffraction shows the high epitaxial quality of the films with Laue fringes (Fig. 1a-e) attesting for their coherent growth. All films display smooth surfaces with atomic steps, characteristic of a layer-by-layer growth (insets of Fig. 1a-e). The (001) BiFeO 3 peak evolves from the left to the right of the substrate (001) peak upon increase of the in-plane pseudo-cubic lattice parameter of the substrate, as observed in the 2θ-ω scans. Reciprocal space maps indicate that the films are fully strained (Supplementary Fig. 1) with only two elastic variants of the BiFeO 3 monoclinic phase ( Fig. 1f-j). Their peak positions enable us to determine a strain value for each film ranging from −1.35% compressive strain to +0.50% tensile strain (Fig. 1k, Supplementary Fig. 1 and Methods).
With this set of structurally equivalent BiFeO 3 thin films, distinguishable only by their strain level, we now focus on the evolution of the ferroelectric and magnetic textures (Fig. 2). In BiFeO 3 , the displacement of Bi ions relative to the FeO 6 octahedra gives rise to a strong ferroelectric polarisation along one of the <111> directions of the pseudo-cubic unit cell. The out-of-plane and in-plane variants of polarisation were identified in each sample using piezoresponse force microscopy (PFM; Methods). For all the samples, the as-grown out-of-plane polarisation is pointing downward, i.e. towards the bottom electrode (Supplementary Fig. 2a). Figure 2a-e displays similar striped-domain structures with two in-plane ferroelectric variants, which correspond to the two elastic domains observed in reciprocal space maps 15 . In contrast to the as-grown striped domain patterns of the BiFeO 3 films grown on the scandates, the striped domain pattern of the BiFeO 3 film on SrTiO 3 was defined by PFM ( Supplementary Fig. 4). All the samples can be considered as a periodic array of 71-degree domain walls, separated by two ferroelectric variants (Supplementary Figs. 2 and 3). This ordered ferroelectric landscape greatly simplifies the exploration and interpretation of the magnetic configuration for each ferroelectric domain 16 .
Influence of the strain on the antiferromagnetic textures. For each sample, the corresponding antiferromagnetic spin textures were imaged in real space with a scanning NV (nitrogen-vacancy) magnetometer 17 operated in dual-iso-B imaging mode ( Fig. 2g-k, Methods, Supplementary Fig. 5). In the strain range of −1.35 to +0.05%, the NV images display a similar zig-zag pattern of periodic stray fields generated by cycloidal antiferromagnetic orders. More precisely, in each vertical ferroelectric domain (separated by dashed lines in Fig. 2g-j), we observe a single propagation direction of the spin cycloid. As the in-plane variant of polarisation rotates from one domain to another, the spin cycloid propagation direction rotates accordingly. This implies a one-to-one correspondence between the ferroelectric and antiferromagnetic domains. In contrast, for large tensile strain (+0.5%) corresponding to BiFeO 3 films grown on SmScO 3 substrates, the cycloidal order appears to be strongly destabilized ( Fig. 2k and Supplementary Fig. 6). In this specific case, the ferroelectric periodicity is lost in the magnetic pattern, which may suggest a weaker magnetoelectric coupling as compared to other magnetic interactions. This strain dependence of the magnetic textures is reminiscent of previous works where antiferromagnetic order as a function of strain was studied by nonlocal techniques such as Mössbauer and Raman spectroscopies 10,11 . Indeed, a canted G-type antiferromagnetic order was identified for tensile strain over +0.5% and a cycloidal order from −1.6% to +0.5%.
In the present sample set, the magnetic image of BiFeO 3 films grown on DyScO 3 substrates ( Fig. 2h) with −0.35% strain corresponds to the configuration already observed by Gross et al. 16 . The 90-degree in-plane rotation of the ferroelectric polarisation imprints the 90-degree in-plane rotation of the cycloidal propagation direction. This corresponds to one of the three bulk-like cycloids (cycloid I) with propagation vectors contained in the (111) plane orthogonal to the polarisation 18,19 (Fig. 3a, b). Among them, the observed k 1 vector lies in the (001) plane of the film, for both ferroelectric variants (Fig. 2h). For lower compressive strain (−0.10%, TbScO 3 ), the magnetic configuration is found to be identical (Fig. 2i), also corresponding to the bulk-like cycloid (cycloid I, k 1 ).
A subtle change of the strain towards the tensile side (+0.05%, GdScO 3 ) greatly influences the magnetic landscape. Indeed, the spin texture can no longer be explained by the bulk-like cycloid as the zig-zag features are no longer orthogonal to each other, but rather at 120 ± 5 degrees (Fig. 2j). Interestingly, for (001) BiFeO 3 films grown under low tensile strain (+0.2%), previous reports have shown evidence for exotic spin cycloids 10,11 . In these works, Mössbauer and nuclear resonant scattering data suggested 20 . 3c, d). In the case of BiFeO 3 thin films on GdScO 3 substrates (Fig. 2j), the angle of the zig-zag pattern is only compatible with alternating k 1 ′, k 2 ′ propagation vectors, giving rise to an angle of 127 degrees, as projected on the film surface. Surprisingly, a similar scenario takes place for large compressive strain (−1.35%, SrTiO 3 ) as the zig-zag angle (Fig. 2g) is the same as for BiFeO 3 grown on GdScO 3 . This unprecedented real-space observation of the cycloid II under both large compressive strain and low tensile strain calls for further theoretical input to explain the interplay between strain and antiferromagnetic textures.
Insights into the different spin cycloids. To further corroborate the nanoscale real-space images of the magnetic arrangements, complementary macroscopic investigations were performed by Xray resonant elastic scattering on BiFeO 3 samples 21,22 grown on both DyScO 3 (cycloid I) and GdScO 3 (cycloid II) substrates (Fig. 4a, c). As the spin cycloid is a periodic magnetic object, it gives rise to a diffracted pattern at the Fe resonant L-edge. In order to select the diffracted signal of magnetic origin, the difference between left and right circularly polarized light is plotted as a dichroic diffracted pattern (Fig. 4a, red and blue correspond to positive and negative dichroism, respectively). In both diagonals from the specular spot, the inverted contrast between +q and −q spots is a signature of chirality. Indeed, BiFeO 3 spin cycloids in which spins rotate in a plane defined by the polarisation (P) and the propagation vector (k) are chiral objects. For BiFeO 3 thin films grown on DyScO 3 , the presence of two orthogonal cycloid propagation directions (red arrows in Fig. 4a) with identical periods gives rise to two orthogonal lines of diffracted spots, thus defining a square diffracted pattern. The fine structure of this pattern is rendered more complex by additional spots that arise from the modulation of the magnetic periodicity by the ferroelectric domain structure; 23 however, here our focus is on the cycloid propagation direction and periodicity. The spacing between the +q and −q spots corresponds to a cycloid period of 72 ± 5 nm for both spin cycloids with k 1 propagation vector. Consistently at the local scale, the combination of PFM and scanning NV magnetometry allows to identify the relative orientation of the ferroelectric polarisation (P, grey arrows in Fig. 4b) and cycloid propagation direction (k 1 , red arrows in Fig. 4b) on both sides of a domain wall. Thus, our microscopic real-space experiments and macroscopic reciprocal-space observations both attest for a single cycloidal vector (k 1 ) in BiFeO 3 thin films under moderate compressive strain.
In contrast, for BiFeO 3 films grown on GdScO 3 imposing slight tensile strain, the dichroic diffracted pattern is no longer square but rectangular (Fig. 4c). Hence, we preclude the above-mentioned scenario with two bulk-like (cycloid I) orthogonal vectors. The two diagonals of the rectangular pattern (green arrows in Fig. 4c) form an angle of about 110 ± 5 degrees, in accordance with the typical angles observed in NV magnetometry images. The only plausible scenario, therefore, corresponds to two types of ferroelectric domains respectively harbouring alternating k 1 ′ and k 2 ′ propagation vectors of the cycloid II, as observed in real space (Fig. 4d). These two cycloid propagation variants appear to be energetically degenerated and favoured over the more out-of-plane k 3 ′ vector (Fig. 3c). Consequently, these cycloidal BiFeO 3 films, under either compressive or tensile strain, exhibit a one-to-one imprint between ferroelectric and antiferromagnetic order.
Electric-field control of antiferromagnetic textures. Beyond the observations on pristine configurations of ferroelectric domains in which the cycloid propagation is locked onto the polarisation, we now manipulate the ferroelectric order using electric fields, with the aim to design antiferromagnetic landscapes on demand. We first use PFM to draw micron-size ferroelectric domains (Supplementary Fig. 7) by virtue of the so-called trailing field 24-26 .
Using microdiffraction experiments, we checked that no strain difference could be detected between artificially written and asgrown striped-domains (Methods and Supplementary Fig. 8). NV magnetometry is then performed on these artificial domains to reveal the corresponding magnetic textures (Fig. 5 and Supplementary Fig. 7). For strain states ranging from −0.35 to +0.50%, single ferroelectric domains always correspond to a spin cycloid with a single propagation vector. For BiFeO 3 films grown on DyScO 3 (−0.35%, Fig. 5a) or TbScO 3 (−0.10%, Fig. 5b), the spin cycloid propagates in a direction perpendicular to the ferroelectric polarisation. This implies that the in-plane k 1 propagation is still favoured, switching from two pristine cycloid Is to a single written cycloid I. Interestingly, the spin cycloid period λ decreases from about 78 ± 5 nm in the pristine (two domain) state to 65 ± 2 nm for the switched (single domain) state. In single domains, the spin cycloid period thus appears closer to that observed in bulk BiFeO 3 (λ bulk = 64 nm, ref. 19 ), suggesting that periodic electric/elastic boundary conditions influence the cycloid period.
For BiFeO 3 films grown on GdScO 3 (+0.05%, Fig. 5c), the spin cycloid propagates horizontally, i.e. at 45 degrees from the inplane polarisation variant of the single ferroelectric domain. This implies that the cycloid I out-of-plane propagation vector (k 2 , Fig. 3a, b) is selected, corresponding to a switching from two cycloid IIs (k 1 ′, k 2 ′) to a single cycloid I (k 2 ). In addition, the apparent cycloid period of 92 ± 3 nm in the single domain is compatible with its projection onto the sample surface  λ), giving rise to an intrinsic period of λ = 65 ± 2 nm, close to the bulk value. These experiments on single domains suggest that strain primarily has an influence on the direction of the bulk-like cycloid propagation (in-plane for compressive and out-of-plane for tensile strains). In the case of BiFeO 3 films grown on SmScO 3 (+0.50%, Fig. 5d), the cycloid is observed to propagate in a direction almost parallel to the inplane variant of polarisation. Considering the three vectors of each cycloid type (Fig. 3), this is only compatible with the k 3 ′ propagation vector of cycloid II. In this case, we find an apparent cycloid period of 146 ± 5 nm leading to an intrinsic period of 84 ± 3 nm (λ surf ¼ ffiffi ffi 3 p λ). The enhanced period compared to the bulk value is here attributed to the significant tensile strain of BiFeO 3 films grown on SmScO 3 (Ref. 11 .). In this latter example, we have demonstrated electric-field switching from a G-type antiferromagnetic order to a cycloidal state.
In this work, we have shown real-space evidence of multiple antiferromagnetic landscapes in BiFeO 3 epitaxial thin films. Depending on the strain level, bulk-like cycloids, exotic cycloids, and G-type collinear order are observed. The exotic cycloid is, rather unexpectedly, shown to exist for two very different strain states: one being compressive and the other tensile. Combining multiple scanning probe techniques, we provide direct correspondence between ferroelectric domains and complex antiferromagnetic textures. These local observations are supported by macroscopic resonant X-ray scattering on both types of cycloids. Although the cycloid is often not considered in the literature of BiFeO 3 thin films 27 , our observations show that only the cycloidal state enables a full one-to-one correspondence between ferroic orders in the native striped-domains as well as in artificiallydesigned single domains. The electric field enables toggling either from one type of cycloid to another or from collinear to cycloidal states. More specifically, we are now able to electrically design single spin cycloids on demand with controlled propagation either in the plane or out of the film plane. This fully mastered magnetoelectric system is an ideal playground to investigate reconfigurable low-power antiferromagnetic spintronic 1,28,29 or magnonic 30 architectures at room temperature.

Methods
Sample fabrication. BiFeO 3 thin films were grown by pulsed laser deposition on various substrates using a KrF excimer laser (248 nm) with a fluence of 1 J cm −2 . Prior to film growth, the scandate substrates (DyScO 3 , TbScO 3 , GdScO 3 , SmScO 3 ) were ex-situ annealed for 3 h at 1000°C under flowing oxygen. The SrTiO 3 substrate was chemically etched with a buffered HF solution before following the same annealing procedure. For all the samples, a SrRuO 3 bottom electrode (3-5 nm) was first grown at 660°C under 0.2 mbar of oxygen pressure with a laser repetition rate of 5 Hz. The BiFeO 3 thin film (30-60 nm) was subsequently grown at the same temperature under 0.36 mbar of oxygen pressure and a repetition rate of 2 Hz. Following the growth of the bilayer, the samples were cooled down to room temperature under an oxygen pressure of 300 mbar.
Structural characterisations. The structural properties of the films were determined by X-ray diffraction (XRD) using a Panalytical Empyrean diffractometer equipped with a hybrid monochromator for Cu K α1 radiation and a PIXcel3D detector. Full 2θ-ω XRD scans (not shown) indicate that all films are single phase with a monoclinic (001) orientation. To gain further insight into the elastic domains and strain of the films, we carried out reciprocal space maps (RSMs) around the (103), (013), (113), and (113) substrate peaks (Fig. 1f-j and Supplementary Fig. 1). The (110) orthorhombic scandates (XSO with X = Dy, Tb, Gd, Sm) are all described in a (001) monoclinic (which is only a slight correction from pseudo-cubic) notation for simplicity 31  The strain values were then estimated by comparing the average in-plane lattice parameter with the volume of the unit-cell as: Considering the small deviation from the cubic unit cell, cell, throughout the manuscript, descriptions of the ferroelectric and magnetic properties are given in the pseudo-cubic perovskite lattice for simplicity.
Piezoresponse force microscopy. The experiments were conducted with an atomic force microscope (Nanoscope V multimode, Bruker) and two external lockin detectors (SR830, Stanford Research) for the simultaneous acquisition of in-plane and out-of-plane responses. An external ac source (DS360, Stanford Research) was used to excite the SrRuO 3 bottom electrode at a frequency of 35 kHz while the conducting Pt-coated tip was grounded. We used stiff cantilevers (40 N m −1 ) for accurate out-of-plane detection and softer ones (3-7 N m −1 ) for the in-plane detection. In all the BiFeO 3 samples, the as-grown out-of-plane signal is homogeneous ( Supplementary Fig. 2a) Supplementary Fig. 7, the phase shift between the in-plane and out-of-plane domains is 180 degrees and the phase scale is fixed at 360 degrees to avoid saturation of the image. Before designing artificial domains in the BiFeO 3 thin films, a radio frequency antenna and markers are defined by laser lithography and lift-off of a Au/Ti sputtered layer ( Supplementary  Fig. 5). These markers are typically less than 10 μm away from the antenna and are visible with an optical microscope. Optical microscopy allows for coarse repositioning, and maps provided by PFM measurements (including markers; Supplementary Fig. 5) are used to precisely relocate NV imaging.
Scanning NV magnetometry. Scanning-NV magnetometry was performed under ambient conditions with commercial all-diamond scanning-probe tips containing single NV defects (QNAMI, Quantilever MX). The tip was integrated into a tuningfork-based atomic force microscope (AFM) combined with a confocal microscope optimized for single NV defect spectroscopy. Magnetic fields emanating from the sample are detected by recording the Zeeman shift of the NV defect's electronic spin sublevels through optical detection of the electron spin resonance 17 . The scanning-NV magnetometer was operated in the dual-iso-B imaging mode by monitoring the signal S = PL(υ 2 )−PL(υ 1 ), corresponding to the difference of photoluminescence (PL) intensity for two fixed microwave frequencies, υ 1 and υ 2 , applied consecutively at each point of the scan through a gold stripline antenna directly fabricated onto the BiFeO 3 sample (see the description before) 17 . Experiments were performed with a NV-to-sample distance of 60 nm and a bias magnetic field of 2 mT applied along the NV quantization axis. The standard error of the cycloid period measurement is limited by the calibration of the scanner.
Resonant X-ray elastic scattering. Resonant X-ray scattering measurements were performed at the Fe L and O K edges using the RESOXS diffractometer 32 at the SEXTANTS beamline 33 of the SOLEIL synchrotron. Data were collected using nearly fully circular left and right X-ray polarisations delivered by the HU44 Apple2 undulator located at the I14-M straight section of the storage ring.
Microdiffraction. The experiments were performed using a Bruker D8 Discover diffractometer with a high brilliance microfocus Cu rotating anode generator, hybrid Montel optics, a 20 µm diameter circular pinhole beam collimator, and an EIGER2 R 500 K area detector. No monochromator was used to maximize the flux from the microfocus lab source, leading to the characteristic K α1,2 peak splitting. Prior to the microdiffraction experiments, a lithographically defined hard mask of 90 nm thick Au with 30 µm wide square openings was applied by sputtering and lift-off for precise alignment and orientation on the sample. Selected areas, written and pristine, with different domain wall densities were first analysed by PFM and subsequently by microdiffraction at the same area to obtain local structural information.

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