Introduction

One major theme in spintronics research is the development of fast and high-density data storage devices controllable by external stimuli and stable against stray magnetic fields. Antiferromagnetic (AF) materials have the potential to satisfy those criteria, because they feature ultrafast spin dynamics due to the absence of the demagnetizing field and can be switched by electrical currents1,2,3,4. The behavior of AF materials under external stimuli has been the focus of intense investigations in the last decades, passing from the indirect exploitation in exchange bias systems of coupled ferromagnetic/antiferromagnetic films5 to a more direct control in AF spintronic devices6. The key challenge for technological implementation is achieving precise control over the AF axis orientation—ranging from fully in-plane (IP) to fully out-of-plane (OOP)—as well as domain size and distribution. Large and homogeneous AF domains with controlled axis alignment are desirable, as they enhance device efficiency by reducing spin filtering losses of magnons propagating across magnetic domain walls7,8,9. While the magnetic domain formation in ferromagnets (F) has been extensively studied10 and is largely governed by the minimization of the demagnetizing field energy, domain formation in AF thin films remains less explored. In the absence of a macroscopic demagnetizing field, AF films commonly exhibit multidomain configurations that are influenced by several factors, such as strain, destressing fields coming from long-range magnetoelastic forces, lattice relaxations, crystalline twins and dislocations11,12,13,14,15,16. Strain, in particular, is a well-established parameter for tailoring the magnetic anisotropy in both F17 and AF18,19 films.

Among AF materials, perovskite oxides have garnered significant attention due to their strong coupling between lattice, charge, orbital, and spin degrees of freedom, making their magnetic properties highly sensitive to epitaxial strain20,21,22,23,24,25. One well-known example is the prototypical insulating/semiconductor orthoferrite LFO26, whose long-range magnetic order is directly linked to its crystallographic structure. Bulk LFO crystallizes in an orthorhombic (space group Pbnm, a = 5.555 Å, b = 5.567 Å and c = 7.855 Å12,27 and can be described as pseudocubic (apc = 3.932 Å)), with a G-type AF order with an easy magnetic axis along the orthorhombic a-axis, i.e., < 100>o, as illustrated in Fig. 1a. The combination of large Fe magnetic moment (~5 µB/Fe28,29), strong interatomic superexchange (J1/kB ≈ 50 K30,31) and high ordering temperature TNéel ~740 K26,30 make LFO a promising candidate for strain engineering when epitaxially grown on lattice-mismatched substrates, similar to other perovskite films20,32,33,34,35. LFO films have mostly been grown both by pulsed laser ablation (PLD)11,36 and molecular beam epitaxy (MBE)12,37,38.

Fig. 1: LFO bulk crystal and thin films under various substrates.
figure 1

a Bulk orthorhombic lattice structure of LaFeO3 with red, green and blue spheres corresponding to Oxygen, Lanthanum and Iron atoms, respectively. AF-axis is highlighted with yellow arrows. b ω-2θ X-ray diffraction measurements performed on LFO films grown under different epitaxial strain conditions (from compressive to tensile strain). The experimental curves are spaced by a constant value on this logarithmic scale. The LFO diffraction peaks are marked by blue lines.

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The most direct technique for spatially-resolving AF properties is X-ray magnetic linear dichroism combined with photoelectron emission microscopy (XMLD-PEEM), as demonstrated in pioneering studies on LFO thin films12,36,38,39. These studies were primarily focused on LFO films grown on cubic SrTiO3 (STO) (001) substrates showing four domains whose AF axes lie predominantly IP, with an OOP tilt of 20 up to 45°, depending on the growth method used12,36,37,40,41. The four AF domains exhibit 90° rotational symmetry, reflecting the symmetry of LFO’s crystallographic twin domains42. Using tailored substrates and different measurement configurations, Lüning et al.12 showed that the AF axes remain always coplanar to the orthorhombic [001] axis. On STO(110) substrates, twin LFO domains persist, aligning their orthorhombic [001] axis in-plane along the cubic [100] or [010] axes of the substrate. This specific configuration results in four AF domains with axes oriented 35° OOP and lying in the plane defined by the orthorhombic [001] and the surface normal, distinct from the bulk LFO but similar to the properties of LFO films grown on STO(001). Recently, K. Kjærnes et al.11 compared the growth of LFO films on (011) and (101)-oriented orthorhombic DyScO3 (DSO), GdScO3 (GSO), and NdGaO3 (NGO) substrates. They found that LFO forms a monodomain structure on DSO and GSO but multiple domains due to strain relaxation on NGO, which has the largest lattice mismatch with LFO. In contrast with bulk LFO, where the AF Néel vector aligns along the shorter [100] axis, LFO films on both DSO and GSO exhibit a Néel vector along the tensile-strained longer <1-10> axis, lying IP or is tilted OOP by 55° depending on the substrate orientation. The authors attributed this counterintuitive observation—perturbing the expected AF superexchange mechanism—to strain-induced variations in Fe-O-Fe bond lengths and angles, which deviate only slightly from bulk values (2 Å ± 0.03 Å and 157 ± 2°). In their study, K. Kjærnes et al.11 performed XMLD-PEEM characterizations at only a few measurement angles, preventing a complete determination of the AF axis orientation and domain distribution across the probed surface. In most of the above-mentioned studies on LFO films, AF domain sizes are typically in the range of a few µm2, except for highly miscut substrates12. These sizes are consistent with what is reported for typical AF domain sizes, in the range from submicron to a few microns square, as observed for NiO43,44, CuMnAs14,45 or La0.7Sr0.3FeO346. Larger AF domains have been observed in a few cases, particularly when the film is strongly strained. For example, LFO deposited on DSO(101) exhibits domains exceeding 400 μm², larger than the probed area, due to a macroscopic uniaxial anisotropy, with the Néel vector oriented in-plane11.

As these studies suggest, AF domain properties and Néel vector orientation are strongly influenced by epitaxial strain. However, interpretations vary among authors, and no unified model currently describes the effect of epitaxial strain on LFO’s AF properties. In this work, we investigate the AF properties of stoichiometric LFO films coherently grown on a variety of substrates, applying different strains along different crystallographic orientations. The films are grown by oxide MBE47,48 using a shuttered growth method, ensuring precise stoichiometry control. This approach produces high-quality films with thicknesses kept below the critical limit for strain relaxation. To determine local AF properties, we perform extensive XMLD-PEEM measurements characterizing domain shape, size and AF-axis orientation. These findings are correlated with the crystallographic axes of the thin film via laboratory X-ray diffraction (XRD) measurements. By spanning a wide range of compressive to tensile strain (average –1.79% to +1.50% depending on the substrate) including both tetragonal/cubic and orthorhombic substrates with different crystallographic orientations, we find that the AF domain configuration is dictated by the substrate crystal symmetry, and the Néel vector orientation is controlled by the magnitude and type of substrate-induced strain. Fully strained films on orthorhombic substrates exhibit a monodomain state whose dimensions exceed the ~80 µm2 field of view (FOV), while cubic substrates mostly lead to multiple AF domains. Furthermore, we observe a transition of the AF axis orientation from fully in-plane to fully out-of-plane as the substrate-induced strain varies from compressive to tensile, independently of the substrate crystallographic symmetry. These findings demonstrate that epitaxial strain enables full tuning of AF properties in LFO thin films, highlighting their potential for AF spintronic devices and providing a framework for strain-engineered control of AF behavior in other materials.

Results and discussion

Crystal details and structural characterizations

In this study, “tetragonal”, “cubic”, “orthorhombic” and “pseudocubic” axes will be denoted with the subscripts “t”, “c”, “o” and “pc”, respectively. Supplementary Note 1 and Table S1 in the Supplementary Information list the investigated substrates, along with their lattice parameters and the expected strain for fully strained LFO films. Cubic and tetragonal substrates, all (001)c/t-oriented, present a square surface net and include (LaAlO3)0.3(Sr2TaAlO6)0.7 (LSAT), STO and BaTiO3 (BTO), with lattice parameters ranging from a = 3.870 Å (LSAT) to 3.991 Å (BTO). These substrates induce biaxial strain in the orthorhombic LFO film, from −1.52% (compressive) on LSAT to +1.50% (tensile) on BTO (see Table S1). In contrast, orthorhombic substrates such as NGO, DSO, and GSO, cut along either (110)o or (001)o, present a rectangular surface net. The induced strain varies from −1.79% (NGO(110)o) to +0.85% (GSO(110)o).

LFO films grown on cubic and tetragonal substrates can adopt two possible configurations, either LFO (001)o or (110)o out-of-plane. While the first case leads to both in-plane LFO (100)o/(010)o strained along substrate (110)c/t and (1-10)c/t, respectively, the second case leads to both in-plane LFO (001)o/(1-10)o strained along the substrate (100)c/t and (010)c/t. The preferred orientation is determined theoretically by the lattice mismatch, with the configuration that minimizes strain being stabilized. As summarized in Table S1, LFO films grow along (110)o on LSAT and STO, whereas on BTO, they are more likely to adopt the (001)o orientation. For the first case, the growth results in two twinned crystallographic domains, with the [001]o axis lying in the surface plane, parallel to either the [100]c or [010]c axes of the substrate. In both domains, the [100]o and [010]o axes are canted with an angle close to 45° OOP12,36,37,49. In contrast, LFO films grown on orthorhombic substrates are expected to form only one crystallographic domain, adopting either (001)o or (110)o orientations, with the film orthorhombic axes aligning with those of the substrate50,51. To facilitate comparisons with existing literature, we use a pseudocubic notation, which simplifies the description of different crystallographic orientations (a schematic will summarize these structures for each experimental case). For cubic substrates presenting a square surface net, the pseudocubic film axes are aligned with those of the substrate. For orthorhombic substrates with a rectangular surface net, the pseudocubic film axes are rotated IP by 45° with respect to the [100]o and [010]o in-plane axes in (001)o-oriented substrates, and are parallel to [1-10]o and [001]o axes in (110)o-oriented substrates. Although LFO films experience biaxial strain on both cubic/tetragonal and orthorhombic substrates, it is often useful to express the average lattice mismatch in pseudocubic notation for easier comparison between different strain states. The limitations of this approximation will be discussed later.

The LFO films grown by MBE are characterized in situ by reflection high-energy electron diffraction (RHEED) measurements (see Supplementary Note 2). The images in Fig. S1 show a strong crystallinity with the expected symmetry. For most substrates, a film thickness of 100 unit cells (u.c.) is used, which is below the critical thickness for strain relaxation52. However, for BTO(001) and NGO(110) substrates, thinner films of 10 and 50 u.c., respectively, were chosen. A thickness of tens u.c. is large enough to minimize the influence of interfacial effects such as mixed termination53 ensuring that strain remains the dominant factor influencing the magnetic order. After growth, XRD measurements were performed to assess the crystalline symmetry, the miscut value and direction, and to evaluate the strain state and quality of the films. All samples were measured with the exception of LFO//BTO(001) due to its reduced film thickness. However, we note that LFO remains strained to the BTO substrate as indicated during growth by the constant full width at half maximum (FWHM) of the diffraction and specular spots in RHEED during growth, reflecting the coherence length of the crystalline structure. Figure 1b shows symmetric ω-2θ diffraction measurements around LFO (002)pc, which reveal a single phase whose peak position changes drastically as a function of epitaxial strain. Under biaxial strain, the film unit cell deforms elastically: when under compressive strain, its out-of-plane lattice parameter becomes larger than that of the substrate (resulting in a diffraction peak at a lower 2θ angle), while tensile strain produces the opposite effect. Laue fringes observed in all LFO peaks indicate a smooth surface and high crystallinity, as confirmed by the XRD rocking curves (see Fig. S2 for films on cubic LSAT(001) and orthorhombic DSO(110) substrates). In these cases, the FWHM of the film peaks matches that of the substrates. Although the a- and b- lattice parameters of LFO are nearly equal, Figure S3 confirms the presence of the structural twin domains with perpendicular IP orientations with the resolution of our laboratory X-ray diffractometer for the LFO//STO case. Figure S4 presents asymmetric reciprocal space maps around the LFO peaks. All thin film diffracting peaks are at the same Q// position value as the substrates' ones, confirming that the LFO films remain fully strained. There is an indication of initial relaxation for the LFO//NGO(110) sample, which experiences the largest strain (see Table S1).

Spectroscopy characterizations of the AF surface

On the LFO//LSAT (001) sample at room temperature (RT), Fig. 2a displays the XA spectra and the resulting XLMD spectrum. Similar spectra are measured for all samples in this study. The L3 edge presents two prominent peaks at 708 eV (labeled A in Fig. 2a) and 710 eV (B in Fig. 2a), in good agreement with spectra previously reported for this compound54,55. The observed spectral features indicate the presence of Fe³⁺ in its high-spin 3d⁵ ground state within an almost octahedral environment, where the A and B peaks mainly correspond to t2g and eg orbitals, respectively. We derive the XMLD spectrum as the difference of LH to LV light polarization and its intensity is similar to that reported by Lüning et al.12. Czekaj et al.36 identify the dichroic signal at first peak of the L3 edge (A) as an indicator of the AF orientation, because its intensity is larger when the X-ray electric field vector \(\vec{\varepsilon }\) of the incoming light is parallel to the AF axis rather than perpendicular to it. This is in contrast with the work of Lüning et al.12, whose assumptions are based on earlier studies on α-Fe2O356. This discrepancy can be explained by an XMLD sign reversal when the AF axis is near or along the <110>pc or <111>pc axis, as is expected for Fe3+ in octahedral symmetry36,57. In the following sections, we do not make any assumption about the XMLD sign but instead use a fitting routine (described later) that follows the self-consistent method of Czekaj et al.36, to determine the Néel axis orientation.

Fig. 2: Spectroscopy characterizations of the AF LFO surface.
figure 2

At RT on the LFO//LSAT (001) system, a typical XA spectra for LH (black) and LV (red) polarizations and the resulting XMLD (green). b XMLD-PEEM images of the surface. The horizontal images are obtained with the same σ sample position for four α X-ray polarization angles: 0° (LH), 30°, 60° and 90° (LV). The vertical images are obtained using a fixed incident X-rays polarization (LH) but varying the position of the sample; 0°, 45°, 90° and 135° clockwise in red, black, blue and green, respectively. Here, the white/dark scale represents the magnitude of the XMLD dichroic signal. In both cases, the incident beam is at a grazing angle of 16°.

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We recorded XA spectra over a large μm FOV, averaging the signal from different domains. In order to probe locally the magnetic surface, we then recorded a series of XMLD-PEEM images. A sketch of the experimental configuration is shown in Fig. 2b. As for the XA measurements, the X-rays incident angle is 16° with respect to the surface plane. The light polarization angle α is defined in Fig. 2b. The XMLD images were obtained at fixed X-ray polarization by subtracting two set of images at two photon energies \({E}_{A,B}\) corresponding to the Fe \({L}_{3}^{A,B}\) peaks (see A and B in Fig. 2a) and then normalizing the subtracted image to their sum (Eq. 1), which coincide with opposite sign peaks of the XMLD:

$${XMLD}=\frac{{I}_{{E}_{A}}-{I}_{{E}_{B}}}{{I}_{{E}_{A}}+{I}_{{E}_{B}}}$$
(1)

Images were taken while scanning the light polarization from linear horizontal (LH, α = 0°) to linear vertical (LV, α = 90°) in steps of 10°. In addition, the sample surface orientation was rotated through four different azimuthal angles in steps of 45° (σ = 0°, 45°, 90° and 135°). The horizontal images along the top show that, as the polarization changes from LH to LV, the overall contrast decreases, indicating a reduction in \({I}_{{E}_{A}}\), and suggesting that the AF axis lies closer to the in-plane direction. While reduced contrast between the different AF domains is observed when σ is equal to 45 and 135°, a clear white/dark contrast is found for 0 and 90°. This contrast reveals the different azimuthal orientation of the AF axis among the different AF domains.

Analysis of the XMLD-PEEM images

Using the various images in Fig. 2, we reconstruct the 3D orientation of the AF domains by plotting the dichroic intensity within the different domains for different polarization angle α (at fixed azimuthal σ angle) and fitting the resulting curve using the formula36,58 (Eq. 2):

$$I\approx {I}_{0}+{I}_{1}{\cos }^{2}{{\rm{\beta }}}$$
(2)

where β is the angle between the light polarization vector \(\vec{\varepsilon }\) and the Néel vector \(\vec{L}\), I0 represents a constant inherent to the difference between the intensity measured in \({E}_{A,B}\) and I1 represents the XMLD maximum intensity and sign. The values of I0 and I1 are energy dependent, but their values can be fixed for all XMLD angular scans done on the same sample by keeping the \({E}_{A,B}\) energies constant. Note that this equation remains an approximation, especially correct for this nearly-cubic symmetry, as detailed in the Supplementary Information (see Supplementary Note 3, Figs. S5 and  S6) and described in refs. 59,60. In the particular case of 3d5 compounds in which all 3d states are half-filled, the effects of distortions are small, making our fit approximation valid. The AF axis direction can be approximatively identified by the angle of maximum XMLD intensity in the polarization scan plots of the four azimuthal scans. A maximum at a small polarization angle α indicates that the AF axis is closer to the in-plane direction (parallel to the sample surface), while a maximum at a higher polarization angle suggests that the AF axis is nearer the out-of-plane direction.

As an example of analysis, we first examine the properties of LFO domains on the STO(001) substrate. Figure 3a displays an XMLD-PEEM image taken with σ = 0°, α = 0°. Figure 3b shows the light polarization angle scans for the four azimuthal angles (experimental data and fits). The resulting AF configuration within the pseudocubic LFO lattice is illustrated in Fig. 3c.

Fig. 3: Spectro-microscopy characterizations of LFO on STO substrate.
figure 3

a XMLD-PEEM images recorded of LFO deposited on STO (001). b Experimental polarization scans (dots) with their cos2β fitting (solid lines) with red, black, blue and green corresponding to σ of 0° (//[010]pc), 45°, 90° (//[001]pc) and 135°, respectively. c 3D AF reconstruction of the Néel vectors using the same colors as the domains (gold, violet, green and red) in the pseudocubic film notations (blue coordinate system).

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When LFO is under compressive strain on STO substrate that has an IP average strain of −0.63%, the XMLD characterization (Fig. 3a) reveals four different oriented AF domains, each covering roughly 25% of the field of view. These domains are identified by different colors (gold, violet, green and red), irregularly shaped, randomly distributed, and range in lateral size from several hundred nm to a few µm. As an example, consider the domain outlined in violet in Fig. 3a. In the graph shown in Fig. 3b (lower right panel), the dichroic intensity for this domain decreases as the polarization angle α increases, for most of the azimuthal angles σ. By fitting the dichroism data from each (α,σ) scan using the cos²β formula (solid lines), we obtain values for I0, I1, and the Néel vector direction. For incident X-rays arriving at σ = 0° (red line, i.e., along [010]pc), this domain shows a maximum of intensity for α = 22.5 ± 2.5°. In contrast, for σ = 90° (blue line, i.e., along [001]pc), the intensity is small and nearly constant. Combining the fits from all four curves, we can determine that the Néel vector direction inside each violet domain is mainly IP, aligned along [010]pc, with a 20−25° OOP tilt (see Fig. 3c, violet arrow). This differs considerably from bulk LFO, whose AF axes are parallel to [100]o, corresponding to a 45° OOP tilt. For the other colored domains outlined in Fig. 3a, the fitted curves in Fig. 3b reveal that the Néel axes are primarily in-plane, aligned along either <010>pc or <001>pc, with an OOP tilt of 22.5 ± 2.5°. The number of AF domains we observe agrees with the previous results of LFO on STO(001) by Scholl et al.37, Lüning et al.12 and Czekaj et al.36, who also reported four AF domains with Néel vector mainly IP with an OOP tilt of 20–45°. This variation is attributed to different epitaxial strains obtained changing the growth method, as seen in similar systems12,36,37,40,41. We note that our experimentally measured OOP tilt corresponds very closely to that reported by Czekaj et al.36.

Similar analysis were performed on all other substrates, however, we only present XMLD-PEEM images taken in the σ = 0°, α = 0° configuration along with the corresponding 3D AF reconstructions (see Fig. 4).

Fig. 4: LFO AF properties on the various substrates.
figure 4

a Tetragonal/cubic, c orthorhombic (001) and e (110) substrates in gray with orthorhombic/pseudocubic LFO films on top in full/empty blue color, respectively. The red direction in each panel indicates the magnetic easy axis of bulk LFO. XMLD-PEEM images recorded and 3D AF reconstruction of the different regions of interest highlighted with different colors on the figures in the pseudocubic film notations for LFO on; b (001) LSAT, STO and BTO, d (001) NGO, DSO and GSO and f (110) NGO, DSO and GSO.

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AF structure under symmetric in-plane biaxial strain

Cubic or tetragonal (001) substrates have a square surface net exerting an isotropic in-plane strain, thus a biaxial strain on the orthorhombic LFO films. Similar analysis for the LFO//LSAT(001) film (Fig. 4b), with a large –1.52% compressive strain, reveals two different AF domains (colored yellow and violet) that have a mainly IP orientation parallel to [001]pc and [010]pc with a smaller 12.5 ± 2.5° OOP tilt than the one observed on STO. Although the domains are similar in size and in distribution, they are more square than those of STO. As it will be discussed later, the larger compressive strain on LSAT likely influences the magnetoelastic energy and thus reduces the OOP tilt compared to STO12,36,37,40,41. Interestingly, while LFO films grown on cubic substrates are typically expected to display four domains, as seen on STO, only two domains are observed in this LFO//LSAT sample. We attribute the reduction from four to two domains to the substrate miscut, which in this case is approximately ~0.6°, larger than the typical ~0.1–0.2°. Such a miscut is known to affect the magnetic properties of LFO38. Lüning et al.12 showed that LFO grown on STO(001) with a 2° miscut along one of the in-plane [100]c direction develops two twinned crystallographic domains with a preferred distribution of the domains with the c-axis parallel to the step edges, leading to an unbalanced distribution between 90° rotated AF domains. Similarly, in our sample, the observed AF domain walls are mostly pinned along the miscut edges (dotted lines in Fig. 4b), which are oriented 45° away from the crystallographic [100]c axis. Moreover, the distance between the AF domains, forming a line-shaped pattern, varies over the probed surface area between hundreds of nm and 2 µm width, much larger than the approximately 40 nm terrace width estimated from the miscut.

In contrast to compressively strained films on LSAT and STO substrates, the 10 u.c. LFO film on tetragonal BTO(001) substrate (Fig. 4b) experiences a significant tensile strain of +1.50%. Under this condition, the LFO film shows a single AF domain with the Néel vector oriented completely OOP with a residual error close to zero, whose dimensions exceed the 80 µm2 FOV. The two ferroelectric domains of BTO do not visibly affect the XMLD images, as the local in-plane strain variations from ferroelastic deformation are insufficient to overcome the dominant average in-plane tensile strain that forces the Néel axis to be normal to the surface plane61. This is evident in all XMLD angular scans, which show a monotonic increase in intensity regardless of the sample’s azimuthal angle (see Fig.  S7a). Since the strain difference between the two possible growth configurations is small, LFO can also grow with (100)o OOP. In this case, only one crystallographic twin is expected, indicating that strain effects override the crystal symmetry in determining the orientation of the AF-axis anisotropy.

AF structure under asymmetric in-plane biaxial strain

(001) orthorhombic symmetry

When LFO films are grown pseudomorphically on substrates with a rectangular surface net such as orthorhombic NGO, DSO, and GSO(001), the in-plane strain becomes asymmetric; the induced average strains are −1.73%, +0.25% and +0.70%, respectively (Table S1). For LFO on NGO(001), pseudomorphic growth produces compressive strain along both the a- and b-axes. In contrast, DSO(001) and GSO(001) create a mixed strain state: compressive along the a-axis (–2.07% and –1.89%, respectively) and tensile along the b-axis (+ 2.57% and +3.29%, respectively). Unlike the multidomain state seen under symmetric in-plane strain, the XMLD-PEEM images on these rectangular net surfaces reveal a nearly monodomain state regardless of whether the average strain is compressive or tensile. In these cases, the majority domain covers at least 75% of the field of view and up to 98% in the most strained sample (see Fig. 4d). The minority domains appear as needle-like features aligned along the substrate’s long axis, i.e., < 010>o, and are relatively small and discontinuous for NGO (~175 nm wide and few µm long) and for GSO ( ~250 nm wide and longer than the probed area). On DSO, they appear randomly oriented (~150 nm large and a few µm long).

For compressively strained LFO grown on NGO(001) (Fig. 4d), only a very small fraction of the field of view (< 2%) shows minority domains that are too small to analyze reliably. Therefore, we focus on the majority domain in the violet region highlighted in Fig. 4b. Polarization scans for this domain (see Fig.  S7b) reveal a monotonically decreasing dichroic intensity as the polarization angle α increases (i.e., scanning from LH to LV). In agreement with results from LFO grown on cubic LSAT and STO substrates, here again, strong compressive strain pulls the AF axis in-plane along <110>o (parallel to <100>pc), with a very small 4 ± 4° OOP tilt as determined from the fits. Similar AF-orientations have been observed in compressively strained LFO when deposited on NGO (011) or (101), but with multiple AF domains11. In contrast, LFO growth on DSO(001) substrate (Fig. 4d) experiences a small average IP tensile strain (+ 0.25%), which actually corresponds to a mixed biaxial strain state. Similar to NGO(001), the disordered minority domains in this case are too small to be analyzed confidently, so we thus focus on the majority domain in the violet region highlighted in Fig. 4d. Analysis of the polarization scans in Fig. S7b indicates that the Néel vector is nearly OOP by ~80 ± 2.5° with an IP projection aligned along the longer [010]o (|| [110]pc) axis. Notably, the XMLD sign is reversed (\({I}_{1} < 0\), as determined by the fitting of Eq. 2) compared to the other samples (see Fig. S8). In principle, the asymmetric IP strain may further lower the crystal field symmetry and alter the critical angle at which the XMLD sign reverses. Additional charge multiplet calculations, including the full generic XA tensor, are necessary to further investigate this correlation between crystal field symmetry and the critical XMLD sign reversal angle, but this is beyond the scope of our work. Upon increasing the tensile strain with the GSO(001) substrate, the AF domains reach a purely OOP orientation in the majority domain (> 75% of the FOV), while the minority AF domains are aligned strictly IP along the longer [010]o axis, similar to LFO on DSO(001). These observations have recently been confirmed by ab initio calculations for different structures of LFO under relatively large tensile strain when deposited on GSO or DSO in the (011) or (101) orientations11.

(110) orthorhombic symmetry

As a second geometry for asymmetric biaxial strain applied to LFO, we consider orthorhombic NGO, DSO and GSO substrates with (110) orientation (Fig. 4f). The induced average strains are −1.79%, +0.36% and +0.85%, respectively (see Table S1). These values are similar to those in the (001) orthorhombic case but are nearly equal along both in-plane axes, eliminating the tensile/compressive mix. The PEEM dichroic images of the LFO film deposited on NGO(110) in Fig. 4f reveal two very large domains, both with an AF-axis IP along the [001]pc, rotated by a few degrees relative to each other. This observation aligns with the general trend where the compressive strain thus pulls the magnetization into the plane of the thin film. The presence of thin-elongated minority domains may indicate the onset of a partial structural relaxation due to the high level of strain, as also evidenced by the XRD characterizations (see Fig. 1 and S4). In contrast, the tensile strain on LFO imposed by the DSO and GSO (110) substrates results in AF monodomains that extend beyond the field of view, similar to the tensile-strained LFO on BTO and GSO(100) substrates (see Fig. 4b and Fig. 4d for comparison). Specifically, the AF axis of LFO//DSO(110) is tilted 60 ± 4° OOP (see Fig. 4f), aligned along the most tensile axis (see Table S1), and the XMLD sign is positive, as observed in most of the experimental cases described previously. The absence of an XMLD sign change further supports the idea that asymmetric IP strain reduces the crystal field symmetry. Furthermore, we note that the strain along the [1-10]o in-plane direction is +0.28%, slightly less tensile than the +0.45% strain along the [001]o. For the more highly-strained LFO//GSO(110) case, the out-of-plane tilt increases to 78 ± 4°. Additionally, an extra straight and small domain is observed whose vector properties closely resemble those of the majority domain (with a 71° tilt OOP). In all cases, the IP projection of these AF axes is aligned along the <001>o, i.e., the axis under highest tensile strain (see Table S1). Except for the NGO that is close to relaxation, all these experimental results show an absence of minority needle domains, a consequence of the relatively uniform strain. Overall, regardless of the substrate’s crystal symmetry, these findings are consistent with the observations reported by Kjærnes et al.11.

Computation of the influence of strain on AF properties

Strain affects spin-orbit coupling (SOC) because SOC is highly sensitive to orbital overlap. As a result, even small changes in the Fe-O-Fe bond lengths and angles can significantly modify the overall magnetocrystalline anisotropy. This effect is evident in the LFO//DSO(001) case (Fig. 4d), where a reversal in the XMLD dichroic sign is observed. To better understand the rotation of the Néel vector from IP under sufficient compressive strain to OOP under sufficient tensile strain, we performed additional analysis, carrying out ab initio density functional theory (DFT) calculations.

Starting from the bulk LFO AF-G type structure, with high-spin Fe magnetic moments M ~ 5 µB/Fe, we analyzed 4 possible magnetization axes, i.e., [100]o, [010]o, [110]o, and [001]o. Results are displayed with solid-colored lines in Fig. 5 (positive and negative values correspond to tensile and compressive strain, respectively). We added on the same figure the experimental values of the AF-axis tilt ranging from IP (//0°) to OOP (//90°) extracted from Fig. 4 and Fig. S7.

Fig. 5: Experimental and computed AF-axis orientations under various substrate-induced strains.
figure 5

Left Y-scale (square dots) and right Y-scale (solid-colored lines) stand respectively for the AF-axis tilts extracted from our various experimental heterostructures and defined from IP (//0°, i.e., parallel to sample surface) to OOP (//90°, i.e., perpendicular to sample surface), and the antiferromagnetic LFO energy states for different spins aligned along various orthorhombic axes, as a function of the average IP strain. Additional sketches obtained after structural optimization highlight that the AF-axis (yellow arrows) mostly lie in IP (OOP) for a compressive (tensile) strain inside the LFO orthorhombic cell (green, blue and red spheres for Lanthanum, Iron and Oxygen atoms, respectively).

Full size image

Our simulations show that the [100]ₒ direction (red line) represents the lowest AF-energy state under compressive applied strain, so the LFO magnetization aligns along this axis. Consequently, for films grown on NGO (001), NGO (110), LSAT (001) and STO (001) substrates, the magnetization is nearly in-plane. At zero strain, the [100]o remains the most stable configuration, in agreement with the bulk AF-state. The simulations describe a switch of the magnetization axis IP from [100]o towards OOP [001]o (i.e., the green line) at tensile strain, with a crossover at an in-plane average strain of approximately +1.0%, which agrees with experimental trends observed on DSO (001), DSO (110), GSO (001), GSO (110) and BTO (001) substrates, although the continuous nature of the reorientation makes it difficult to pinpoint an exact crossover value. These results are consistent with the effect of in-plane strain on the 3d orbital charge distribution and the resulting p–d hybridization in oxide perovskites62,63. Also, for this volume, the calculated energy difference between [100]o and the most competitive [001]o direction is approximately 30 μeV/f.u. = 7.9 × 104 J/m3, indicating a robust magnetocrystalline anisotropy. This value is larger than that of ferromagnetic bulk bcc Fe (4.8 × 104 J/m3) but lower than the anisotropy observed in hexagonal ferromagnets, where it can be an order of magnitude larger.

Conclusions

By locally reconstructing the 3D orientation of the AF domains in various LFO films under different substrate-driven strain conditions, we are able to determine experimentally how strain and crystallographic properties affect domain populations and Néel vector orientation. LFO films grown on cubic substrates like STO with a square surface net typically exhibit a fourfold distribution of AF domains, but can be controlled by varying the substrate miscut. In contrast, we observe monodomain LFO films on all orthorhombic substrates and under large strain on BTO(001). Regardless of the substrate symmetry, strong compressive strain forces the Néel vector completely in-plane, while strong tensile strain aligns it completely out-of-plane. At intermediate strain levels, the Néel vector gradually rotates between these extremes, with its in-plane projection aligning along the most strained axis in tensile cases. We also observe a sign reversal of the linear dichroism under asymmetric IP strain when the averaging is near zero. Overall, growing coherently-strained stoichiometric LFO films with a wide range of substrate-induced strains enables the creation of monodomain configurations with nearly any desired axis orientation from entirely in-plane to entirely out-of-plane. These findings provide crucial insights into the strain control of antiferromagnetic materials, offering a framework for tuning AF properties in other compounds and paving the way for new AF-based devices.

Methods

Experimental details

The LFO films are grown by MBE using the shuttered technique developed by the Schlom group48,64,65,66. This method alternates the A-site and B-site fluxes of the ABO₃ perovskite, reproducing the unit cell’s layered structure. During growth, in situ RHEED images are continuously recorded and the diffracted intensity oscillations are followed, enabling precise real-time control of the Fe:La stoichiometry and surface structural properties47,48. XRD measurements were performed using a PanAnalytical X’Pert Pro diffractometer (Cu-\({K}_{\alpha }\) wavelength). XA and XMLD-PEEM measurements were performed at the I06 beamline of Diamond Light Source at RT, i.e., in a temperature range well below the Néel temperature of LFO thin films12,36,37. XA spectra are collected across the Fe L₂,₃ edges for both LH and LV polarization, and in total electron yield mode with a probing depth of ~3–5 nm over several hundred µm FOV67. We define horizontal (LH) and vertical (LV) polarization as being parallel and perpendicular to the sample surface, respectively. The resulting XMLD spectra is obtained by subtracting two XA spectra taken with LH and LV. On the other hand, XMLD-PEEM images were taken at Fe L3 edge, using linearly polarized light, in total electron yield mode combined with an Elmitec SPELEEM-III microscope, on a 10 μm field-of-view with a lateral resolution of approximately 100 nm.

Theoretical details

First-principles calculations are performed using the Vienna ab initio simulation package (VASP)68. Projected augmented wave method is used with a cut-off energy of 600 eV; the energy functional includes generalized gradient approximation with an added Hubbard interaction (GGA + U), with on-site Coulomb repulsion of U = 4.3 eV for the Fe 3d states, similarly with existing literature11,69,70,71,72. A Γ-centered Monkhorst-Pack grid of 7 × 7 × 5 k-points is used for self-consistent calculations. Atomic coordinates are relaxed within a force convergence threshold of 1 meV/Å. To simulate the effect of strain on bulk LFO, we simultaneously and symmetrically changed the in-plane lattice parameters ([100]o and [010]o, of the Pbnm cell) over an interval of ±2% average strain. This configuration is slightly different from the geometries in our experiments, but is both qualitative and representative for extending the analysis to our various geometries. Furthermore, the substrate symmetry does not play the major role in determining the AF-axis orientation. For each fixed set of in-plane lattice parameters, the OOP lattice parameter and all the atomic positions were allowed to relax to their minimum energy configuration. For each relaxed structure, we carried out non-collinear spin calculations including SOC to analyze the magnetization. To determine the preferred magnetization direction, we used a VASP feature that fixes the magnetization direction along a specified axis while allowing the magnetic moments to relax self-consistently to minimize the electronic energy. The lowest antiferromagnetic LFO energy state corresponds to the most stable spin alignment.