Shear Strain Control of Multiferroic Magnetic Ordering for Giant Ferromagnetism

doi:10.21203/rs.3.rs-4956109/v1

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Shear Strain Control of Multiferroic Magnetic Ordering for Giant Ferromagnetism

https://doi.org/10.21203/rs.3.rs-4956109/v1

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The magnetic ordering of perovskite ferroelectric oxides is essential for enhancing their stability and minimizing energy losses in magnetoelectric devices. However, inducing a transition from a magnetically disordered state to an ordered one remains a formidable challenge. Here, we propose a chemical sulfurization method that significantly bolsters the magnetic ordering of multiferroic super-tetragonal phase BiFeO₃ thin film, thereby enhancing the magnetic properties. The sulfured films exhibit a robust magnetic transition temperature of 586 K. The remanent magnetization increases approximately 1.6 times in the out-of-plane direction and an impressive 62 times in the in-plane direction. Additionally, the magnetic easy axis transitions from the out-of-plane to the in-plane direction. The X-ray absorption spectroscopy and atomic scale investigation reveal a reconfiguration of the local electronic hybridization states in the film. The sulfur-induced shear strain is identified as the catalyst for a shift in the Fe–O hybridization, from the pyramid-like geometry of FeO₅ to the octahedral arrangement of FeO₆. This transformation is deemed the root cause of the observed magnetic transition in the films. This sulfur-induced strategy for electronic hybridization reconfiguration is expected to break new ground, offering innovative methodologies for modulating perovskite oxides, two-dimensional ferroelectric films, and other ferromagnetic functional thin films.

Physical sciences/Physics/Condensed-matter physics/Ferroelectrics and multiferroics

Physical sciences/Physics/Condensed-matter physics/Magnetic properties and materials

Physical sciences/Chemistry/Materials chemistry/Magnetic materials

magnetic ordering

BiFeO3

sulfurization

shear strain

Perovskite oxides, represented by the ABO₃ structure, are celebrated for their distinctive crystal and electronic structures ^1–7. These unique configurations engender sensitive and controllable spin-lattice-orbit interactions, which imbue these materials with significant potential for scientific research and engineering applications ^8–12. However, the intrinsic properties resulting from the inherent structure of the material that often limit the potential for further development. For example, the star material room-temperature multiferroics, BiFeO₃. Although it has been reported to have long-range ordered ferroelectric polarization, the use of effective ways to transform its inherent antiferromagnetic order is also of great research importance to further exploit its application potential.

BiFeO₃ is a notable room-temperature multiferroic material, classified as a type-I multiferroic ^{13, 14}. This classification indicates that its ferroelectric and ferromagnetic orderings occur independently. The ferroelectric order parameters are related to the 6s² lone-pair electrons of Bi^{3+ 15}, while the ferromagnetic order is associated with the spin configuration of 3d orbitals of Fe³⁺ in the BiFeO₃ ¹⁶. Within its structural framework, the oxygen anion engages in strong electronic hybridization with B-site cations and simultaneously participates in complex electronic interactions with A-site cation ¹⁷. Consequently, the substitution or modulation of the oxygen anion can exert a dual influence, affecting both the A–O and B–O hybridization states and impacting the overall material structure and properties ^{18, 19}. In our previous study, we found of the ferroelectric order parameters can be modulated in [001]-oriented pseudo-cubic epitaxial BiFeO₃ thin films ¹⁸. This modulation was achieved through the strategy of introducing sulfur anions, leading to sulfur-induced rotation of polarization state. In the anion substitution of other systems (e.g. SrNbO₃), the structural and electronic can be modulated through nitrogen doping, showing the mechanism behind a significant metal-to-insulator transition ²⁰. These findings, along with an increasing number of studies, highlight the critical role of anion modulation. This modulation significantly influences in the crystal structure, electronic structure, and physical properties of perovskite oxides thin films, thereby broadening the scope for the development of materials with innovative and unique properties.

Here, we propose a novel strategy for modulating the magnetic properties of perovskite oxide thin films through introducing shear strain via sulfurization. The structural and ferromagnetic orderings of large c/a ratio super-tetragonal BiFeO₃ (T’-BFO) epitaxial films were successfully modulated by sulfur-induced shear strain. A remarkable finding was sulfurization-induced rotation in the ferromagnetic ordering direction of T’-BFO thin films, which resulted in enhanced magnetic collinearity. Additionally, this process was characterized by a shift in the direction of the easy magnetic axis from out-of-plane to in-plane. This anion modulation approach, which introduces shear strain, is broadly applicable to most perovskite oxide, which holds the potential to modulate localized electronic hybridization states, offering new pathways to explore magnetic ordering phenomena in oxide materials.

The magnetic properties of BiFeO₃ originate from the spiral spin configuration in the 3d orbitals of Fe ions ²¹, which exhibit a periodic long-range antiferromagnetic order between the neighboring Fe ions along the [111] direction ²², resulting in a macroscopic magnetic moment that approximates zero ²³. However, the antiferromagnetic order can be rearranged due to the lattice structural distortion. The BiFeO₃ thin film characterized by a tetragonal-like structure and a large c/a ratio represent a significant variant within their systems, which breaks the original antiferromagnetic order and exhibits weak ferromagnetism under the influence of substrate clamping strain and structural deformation ²⁴. Based on that, we hope to induce structural distortion ⁶ and modify the electronic hybridization of Fe ions with surrounding anions in the thin films by introducing shear strain through sulfurization (Fig. 1a). This approach is intended to trigger a reconfiguration of the electron spins of Fe ions, thereby facilitating a transformation in the magnetic ordering of thin films. In addition, the spin cycloid of the bulk BiFeO₃ along the [1–10] direction ^{9, 25} is susceptible to the effects of substrate clamping strain and sulfurization, which may regulate the magnetic axis direction of the thin film.

As shown in Fig. 1b, the magnetic moment of Fe ions generates two distinct components along the out-of-plane and in-plane directions, resulting in magnetic anisotropy ^{26, 27}. It means that the different magnetic fields are required to reach saturation magnetization in out-of-plane and in-plane directions, and the direction requiring a lower magnetic field is the easy magnetization axis. Here, the advisable sulfurization method has been applied to the BiFeO₃ thin film with a large c/a ratio tetragonal-like structure ²⁸, introducing the shear strain and provoking the redistribution of Fe–O hybridization states. This also presents an opportunity to obtain the large saturation and remanent magnetizations in the sulfured T’-BFO thin film (O-BFOS) (Fig. 1c). It is worth noting that this enhancement of the magnetic properties is inseparable from the increase of the magnetic collinearity in the O-BFOS thin film according to the Landau phenomenological theory ^{29, 30}. This is complemented by an increase in the energy barrier required for magnetization, leading to a more dispersed energy distribution in the film after sulfurization (Fig. 1d). Hence, this strategy can maximally preserve the hysteresis while maintaining high magnetization, which is significant for regulating the magnetic properties of BiFeO₃ films.

T’-BFO thin films were epitaxially grown on (001)-oriented LAO substrates by radio-frequency (RF) magnetron sputtering. Figure 2a shows the out-of-plane synchrotron XRD patterns of both the T’-BFO and O-BFOS. The XRD patterns of the T’-BFO film indicated an out-of-plane lattice constant c ≈ 4.66 Å and a c/a ratio ≈ 1.23, suggesting the successful fabrication of the super tetragonal-like phase structure of BiFeO₃ films ^31–33. The absence of additional diffraction peaks in the XRD pattern except for the (00l) diffraction peaks of the film and the substrate, confirms that both the T’-BFO and O-BFOS film are the single-phase epitaxial films. The T’-BFO and O-BFOS film thicknesses were 78 nm and 80 nm, respectively (Figure S1). This indicates that the sulfurization process had a negligible influence on the macroscopic thickness of the films. Notably, the out-of-plane diffraction peaks of the T’-BFO films shift to a higher angle following sulfurization, a phenomenon also observed in sulfured pseudo-cubic phase BiFeO₃ films ¹⁸. This shift not only demonstrates the successful sulfurization in T’-BFO films, but also suggests that the incorporation of S anions induces lattice strains as well.

To substantiate the effect of sulfurization on the symmetry of the films, Φ scans were performed on (101) plane of the T’-BFO, O-BFOS film, and LAO substrate. As illustrated in Fig. 2b, all scans exhibit four diffraction peaks following a 360° rotation, with equal angular spacing of 90°, indicative of a fourfold symmetry. This pattern confirms that T’-BFO films can form a good match with the LAO lattice when grown epitaxially on (001)-oriented single-crystal LAO substrates, and this epitaxial relationship persists even after sulfurization. This finding is highly consistent with the phenomenon observed in STEM (Figure S2). Notably, the Φ scanning diffraction peak of the T’-BFO film undergoes a slight splitting, resulting from the a monoclinic tetragonal-like phase as reported in the literature (M_C-phase) ^{34, 35}.

Subsequently, the RSM around (103) reflections of the T’-BFO and O-BFOS thin films are performed to further investigate their crystal structure (Figure S3). The results show that the sulfurized O-BFOS film experienced compressive strain in the out-of-plane direction, with in-plane relaxation, suggesting a distortion of the lattice structure due to the sulfurization effect. As depicted in Fig. 2c, high-resolution RSM mappings of the (103) reflections of the T’-BFO and O-BFOS thin films were compared. It was observed that the T’-BFO film displayed three distinguishable diffraction points in the (103) RSM mapping, a consequence of its monoclinic distortion along the [100] direction relative to the tetragonal phase, characteristic of a typical monoclinic M_C-phase film. Interestingly, the (103) RSM mapping of the O-BFOS film tends to evolve into an elliptical shape, indicating the diminishing monoclinic distortion along the [100] direction. This leads to the different in-plane lattice constant for a ≠ b (Fig. 2d), inducing a transformation to orthorhombic phase (O-phase), indicating that the introduction of S anions induces lattice distortion through chemical strain. In summary, the bulk R-phase BiFeO₃ was epitaxially grown by RF magnetron sputtering on a (001)-oriented LAO substrate, and the structural distortion of BiFeO₃ tends to form a monoclinic M_C-phase due to substrate clamping strain. Subsequently, introduction of chemical strain through sulfurization causes further structural distortion, leading to the formation of the O-phase.

Fast Fourier transform (FFT) patterns of O-BFOS films along the a-axis direction further confirms the films’ transition to the O-phase after sulfurization, as observed in the microscopic morphology. The FFT analysis for regions b and c reveals a superlattice diffraction spot at (1/2 1/2 1/2), indicated by the red circle in Figure S4, in addition to the FFT for region a, which provides significant evidence for the O-phase transition. STEM energy dispersive X-ray spectroscopy (EDXS) mapping further confirms the successful sulfurization of the T’-BFO film and shows that the S anions are uniformly distributed throughout the films (Figure S5a). By comparing the absorbed energy intensity of individual elements, the S anion content in the film is estimated to be approximately 0.48% (Figure S5b). It is well known that the properties of BiFeO₃-based thin films are intimately related to their lattice structure. The lattice distortion induced by sulfurization alters the hybridization state between the anions and cations in the films, thereby affecting the associated physical properties. Consequently, the modified films are expected to exhibit the novel physical properties characteristics.

Considering that intrinsic BiFeO₃ is a multiferroic material possessing both ferroelectricity and G-type antiferromagnetism, but the c/a ratio of the film increases significantly under biaxial clamping stress, showing a tetragonal-like phase with a large axial ratio. It has been reported that the remanent polarization of the film can reach about 130 ~ 150 µC cm^{− 2 36, 37}. The optical second-harmonic generation (SHG) indicates that the ferroelectricity of the T’-BFO films is relatively weakened after sulfurization (Figure S6) ³⁸. Even so, the sulfurized O-BFOS films with a large axial ratio should also indicate robust ferroelectric properties. In addition, the SHG intensity of T’-BFO and O-BFOS films were also measured in s-out and p-out modes, which were obtained by varying the analyzer polarization vertical or parallel to the incident light field, respectively (Fig. 2d). The s-out patterns of the T’-BFO and O-BFOS films show distinct peaks near 45°, 135°, 225°, and 315°, which can be attributed to the fact that the films have 4mm symmetry. The change of peaks in the p-out indicates that sulfurization causes a tendency for the film to shift from dual rotational symmetry to quadruple symmetry, which also responds to the effect of sulfur anion-induced stress on the structure of the film.

The M_C- and O- phases were analyzed based on the large-scale high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) images along the [100] zone axis (Fig. 2e1 and 2f1). The inverse FFT lattice fringes in both in-plane and out-of-plane directions clearly show the difference between the two structures before and after sulfurization (Fig. 2e2, e3, f2, and f3). Additionally, the shrinkage of lattice parameters in the in-plane and out-of-plane directions after sulfurization are also consistent with the trends of RSM and XRD. Specifically, The M_C-phase exhibits a pronounced wave shape in the in-plane direction (Fig. 2e2), while the O-phase is characterized by a long, straight line (Fig. 2f2), confirming that sulfurization leads a transition towards the more symmetrical O-phase. Subsequently, the strain states in the in-plane and out-of-plane directions of the M_C- and O- phases were quantified using geometric phase analysis (GPA). The GPA mappings shows that the O-phase is subjected to higher compressive strain in the in-plane direction compared to the M_C-phase (Fig. 2e4, f4) and lower tensile strain in the out-of-plane direction compared with M_C-phase (Fig. 2e5, f5). These findings not only highlight the impact of chemical strain from sulfurization on the lattice structure but also provide an important support for the origin of the improved magnetic ordering of the films.

The magnetic hysteresis loops of the films were measured at 300 K by a Magnetic properties measurement system (Fig. 3a, b), indicate that the films before and after sulfurization exhibit significant ferromagnetic properties. It can be observed that both films are magnetically anisotropic before and after sulfurization. Notably, the saturation magnetization of the O-BFOS film is larger than that of the T’-BFO film both in the out-of-plane and in-plane directions. The zero-field cooling (ZFC) and field cooling (FC) curves show that the T’-BFO and O-BFOS films gradually becomes paramagnetic with the increasing temperature, and the macroscopic magnetic moment approaches zero (Fig. 3c). Their magnetic ordering temperatures can be obtained by derivation of FC curves for T’-BFO and O-BFOS films, which are 573 K and 586 K (Fig. 3d), respectively. The results show that sulfurization can enhance the magnetic transition temperature of the films, which is much higher than the room temperature. Moreover, this result is also in general agreement with the reported transition temperatures calculated using Monte Carlo method (MC) ³⁹. The MC shown that the higher the magnetic transition temperature of the film increases with the increase of the in-plane lattice constant a/b in M_C-phase T’-BFO films, which could also be a potential reason for the increase in the magnetic transition temperature of O-BFOS films after sulfurization ^{39, 40}.

The changing trend of the magnetic properties after sulfurization is demonstrated in Fig. 2e. The saturation magnetization of the O-BFOS film in the out-of-plane direction is enhanced from 23.6 to 28.3 emu cc^− 1, which is about 20% higher than that of the T’-BFO film, whereas the enhancement is from 22.3 to 29.5 emu cc^− 1 in the in-plane direction, which is about 32% higher. However, the enhancement of remanent magnetization of the O-BFOS film even more remarkably compared to saturation magnetization changes. In the out-of-plane direction, the remanent magnetization of the O-BFOS film increases to 5.7 emu cc^− 1, which is 1.6 times that of T’-BFO. In the in-plane direction, the remanent magnetization increases by 62 times to about 13.3 emu cc^− 1, demonstrating that sulfurization has a significant effect on the magnetic properties of the film. Remarkably, sulfurization not only reduced the saturation magnetic field of the T’-BFO film in the in-plane direction by one-third, from 1.8 T to 1.2 T, but also increased the saturation magnetic field in the out-of-plane direction to 1.8 T, ultimately leading to a shift of the magnetic easy axis of the film from the out-of-plane to the in-plane direction (Figure S7 and 2f).

We provide direct evidence for ferromagnetic behaviors, magnetic anisotropy, and magnetic easy axis flipping in thin films by obtaining X-ray absorption spectroscopy (XAS) of Fe L-edge. As shown in Fig. 4a, the detection of Fe L-edge XAS using left and right circularly polarized light to verify the spin magnetic moment and magnetic anisotropy of Fe in thin films. Due to the difference in the density of spin-up and spin-down electronic states around Fe ions in thin films, there is a difference in the absorption of left- and right-spin circularly polarized X-rays, resulting in the phenomenon of X-ray magnetic circular dichroism (XMCD) ⁶. The Fe L-edge XAS and XMCD spectra in the T’-BFO and O-BFOS thin films measured under out-of-plane and in-plane magnetic field are shown in Fig. 4c,d. The XMCD patterns, observable with the magnetic field aligned along either direction, confirming that the films' magnetism arises from the electronic spin magnetic moments of Fe, indicating magnetic anisotropy.

The shift of magnetic easy axis direction of the sulfured film from the out-of-plane direction to the in-plane direction was further verified by X-ray magnetic linear dichroism (XMLD) ⁴¹. As shown in Fig. 4b, the Fe L-edge spectra of the T’-BFO and O-BFOS thin films were obtained by keeping the direction of the linearly polarized light as horizontal linear polarization, changing the angle between the film and the X-rays to 30° and 90°, respectively, and applying a magnetic field along the direction of the X-rays. Furthermore, the in-plane and out-of-plane orbital information were obtained by I_ab = I_90° and I_c = (I_90° - I_30°sin²30°)/cos²30°, respectively. As shown in Fig. 4e,f, the variation indicates that the coordination environments of Fe ions are differ between the in-plane and out-of-plane directions, thereby confirming the presence of magnetic anisotropy in the films both before and after sulfurization ^{42, 43}. Meanwhile, it can be observed that the XMLD spectra of T’-BFO and O-BFOS films are completely different (Fig. 4g). The XMLD spectra of the T’-BFO film shows a trend of first increasing, then decreasing and then increasing, while the XMLD of the O-BFOS film shows the opposite trend. The magnetic properties of the BiFeO₃-based films originate from the electron spin of the Fe 3d orbitals, and the orientation of the magnetic easy axis is closely related to the hybridization between the Fe 3d and the nearby O 2p orbitals ^{44, 45}. Accordingly, the differences in the directions of the three peaks A, B, and C in the Fig. 4g indicate the alteration of the electronic hybridization states of Fe ions for both in-plane and out-of-plane directions in the T’-BFO and O-BFOS films. This observation serves as compelling evidence supporting that sulfurization induces a reorientation of the easy magnetic axis in the O-BFOS films from the out-of-plane to the in-plane direction ⁴⁶.

In general, the lattice distortion or rotation of the BO₆ octahedron in the ABO₃-type structure will initiate a change in the local electronic structure, which leads to the fundamental differences in the macroscopic physical properties of the films ^47–49. For the T’-BFO film, the c/a can reach to ~ 1.23 causing Fe ions to offset from the centra of the FeO₆ octahedron due to the LAO substrate clamping stress exceeding 4.5%, resulting in a greatly weakened hybridization of Fe ions with O ions at the bottom of FeO₆ octahedron to form the pyramid-like of the FeO₅ structure (Figure S8). At the same time, the valence of the Fe ion tends to + 2 and the t_2g and e_g orbitals in the Fe L₃ and L₂ edge of the T’-BFO film towards merging (Fig. 5a). In contrast, the absorption peaks of Fe L₃ and L₂ edge of the O-BFOS film exhibit significant splitting compared to that of the T’-BFO film, suggesting that Fe ions in the O-BFOS film is trivalent. The O K-edge absorption spectra consist of three peaks, a, b, and c, which represent the hybridization of O 2p with Fe 3d, Bi 6sp, and Fe 4sp orbitals, respectively ⁴⁴. The change of the ‘a’ peak in the film before and after sulfurization is similar to the trend of the Fe L-edge XAS. Furthermore, a decreasing trend is observed for the ‘c’ peak in the O-BFOS film, which further indicates that the local electronic structure surrounding Fe ions is modified under the effect of sulfurization. This modification suggests that the lattice distortion induced by sulfurization increases the hybridization of the Fe ions with the anions. As a result, the Fe ions experience increased electron loss, shifting their oxidation state towards + 3 in the O-BFOS film, and the electron hybridization reverts to the FeO₆ octahedral configuration.

The outermost electron orbitals of Fe atoms possess eight free electrons which are arranged in the 3d and 4s suborbital with six and two electrons, respectively. The valence state of Fe ions tends to the + 2 in the T’-BFO film ⁵⁰, indicating preferential loss of two electrons in the 4s suborbital. The 3d suborbital can be subdivided into five orbitals, according to the Hund’s rule and the principle of energy minimum, the remaining six electrons will preferentially occupy the five orbitals and the last electron will be paired in the lowest orbital, so that only other four d-suborbital o have the same direction of the electron spins and produce a combined magnetic moment. However, sulfurization in the O-BFOS film leads to a tendency for Fe ions to adopt + 3 valence state, with the remaining five free electrons precisely occupying the five d-suborbitals with the same spin direction. This alignment results in a significant enhancement of the macroscopic magnetism of O-BFOS films when compared to the T’-BFO films.

Additionally, the Fe ions in T’-BFO films hybridize with the neighboring O ions under strong in-plane compressive stresses to form pyramid-like of the FeO₅ structure. The magnetic easy axis of the Fe ion is in the out-of-plane direction due to its closest distance and maximum hybridization with the top O ion, which makes it easier for the outermost electrons of the Fe ion to spin around the out-of-plane direction and generate magnetic moments (Fig. 5b). Subsequently, Fe ions are driven back to FeO₆ octahedral hybridization with the neighboring O ions by sulfurization. Importantly, the lattice of the O-BFOS film relaxes in the in-plane direction due to S ions, which leads to increased hybridization of Fe ions with in-plane O ions while rotating the outermost electrons around the in-plane direction, thus tilting its easy magnetic axial more towards the in-plane direction (Fig. 5b). At the same time, the increase of the in-plane lattice parameter a/b directly leads to the increase of T_C ^{39, 40}.

To investigate the evolution of electronic and magnetic properties upon anion doping, we have performed spin-polarized density functional theory (DFT) calculations with the inclusion of spin-orbit coupling (SOC). Since O-BFOS has the orthorhombic structure, we calculated the total energies of the model by orientating the spins in different directions of [100], [010], and [001]. The energetic profile is shown in Fig. 5c, with the lowest-energy state aligned along the [100] spin direction, which serves as the energy reference set to zero. This indicates that the preferred magnetization axis of O-BFOS is [100], which is consistent with our experiment. We further visualized the charge density difference for both T’-BFO and O-BFOS in Fig. 5d. By observing the significant change of the density difference around anions, we can find that the doping of S lead to the increase of the acquired electrons compared to the pristine T’-BFO. This increase suggests an elevation in the oxidation states of Fe ions and enhanced hybridizations between Fe ions and the anions. The enhancement of charge transfer in O-BFOS is also consistent with what we observed above. The sulfur-induced chemical strain is not only reflected in the effect on the lattice structure of the film, but also has a strong influence on the local electronic structure of the film, which in turn leads to fantastic changes in its physical properties due to the coupling of multiple factors.

In conclusion, the effective modulation of magnetic order in super tetragonal phase T’-BFO films was achieved through shear strain induced by sulfurization. This process demonstrated the transition of the film structure from a monoclinic tetragonal phase to an orthorhombic phase in the presence of sulfur anions. The origin of the sulfur-induced enhancement in the degree of magnetic ordering and the rotation of the easy magnetic axis was further investigated through the strong correlation observed between changes in lattice structure and local electronic hybridization, as evidenced by the techniques such as XMLD, XMCD, and atomic scale imaging. Furthermore, anion substitution engineering can be broadly extended to explore the local structure, magnetic ordering, and ferroelectricity ordering of perovskites. It holds the potential to revolutionize the current landscape of multiferroic and magnetoelectric materials, paving the way for the development of advanced materials with tailored properties for various applications in electronics and spintronics.

Thin-film synthesis: The epitaxial T’-BFO thin films were grown on single-crystalline (001) LAO substrates by using a radio frequency (RF) magnetron sputtering system (VJC-300, Beijing VNANO Vacuum Technology CO., LTD.). The LAO substrates have the lattice parameter of a = b = c = 3.79 Å while the pseudo-cubic bulk BiFeO₃ possesses the lattice parameter of a = b = c = 3.96 Å. The epitaxial growth of BiFeO₃ thin films on LAO substrates results in a significant lattice mismatch, causing substantial in-plane compressive strain of approximately 4.5%. These strain conditions lead to an expansion of the out-of-plane lattice constant, forming tetragonal-like films with large c/a ratios, denoted as T’-BFO. First, the epitaxial T’-BFO thin films were grown at 0.4 Pa and 500 ℃ under an O/Ar = 3:1 atmosphere. The sputtering time was 60 min, followed by in situ annealing for 20 min to obtain T’-BFO films. The anion substituted thin films were prepared through a secondary treatment. A 0.2 M thiourea solution, dissolved in ethanol and water (solvent volume ratio of 4:1), was spin-coated onto the T’-BFO thin films at 3000 rpm, followed by pyrolysis at 350 ℃ for 5 min and annealing at 600 ℃for 20 min to obtain the O-BFOS thin films.

Structural and chemical characterization

The structure, thickness, and orientation of the thin films were investigated via synchrotron XRD, XRR, and RSM measurements, which were conducted at the Diffuse X-ray Scattering Station of the Beijing Synchrotron Radiation Facility (BSRF-1W1A). Besides, XAS measurements were performed at the photoelectron spectroscopy station of BSRF-4B9B.

Electron microscopy analyses

The STEM experiments were performed with a 200 kV JEOL ARM electron microscope equipped with double aberration correctors. The STEM–EDXS experiments were conducted at 200 kV with the Super EDS detectors. Geometric phase analysis (GPA) be used to estimate the spatial distribution of strain by combining the Real-space and Fourier-space information of the STEM images.

Magnetic measurements

The magnetic field-dependent magnetization (M-H) loops were measured using a Quantum Design magnetic property measurement system (MPMS XL-7) in the temperature range of 10–700 K with the magnetic field applied along the in-plane and out-of-plane direction of the substrate and were obtained after subtracting the diamagnetic background of the substrate. It should be noted that the ZFC-FC were measured at an out-of-plane magnetic field of 1000 Oe, thus resulting in a lower ZFC-FC curve for the O-BFOS than that of the T’-BFO film. XMCD and XMLD characterizations were performed in total electron yield mode at Beamline BL07U and BL08U at Shanghai Synchrotron Radiation Facility. Due to the difference in the density of spin-up and spin-down electronic states around Fe ions in thin films, there is a difference in the absorption of left- and right-spin circularly polarized X-rays, resulting in the phenomenon of XMCD. XMCD measurements were collected in total electron yield (TEY) mode at 300 K with the magnetic fields of H = 6000 Oe. For the XMLD, the Fe L-edge spectra of the T’-BFO and O-BFOS thin films were obtained by keeping the direction of the linearly polarized light as horizontal linear polarization, changing the angle between the film and the X-rays to 30° and 90°, respectively, and applying a magnetic field (H = 4000 Oe) along the direction of the X-rays. Furthermore, the in-plane and out-of-plane orbital information were obtained by I_ab = I_90° and I_c = (I_90° - I_30°sin²30°)/cos²30°, respectively. The XMLD spectra can be obtained by making a difference between the Fe L-edge XAS spectra obtained at I_c and I_ab, denoted as I_XMLD = I_c – I_ab.

SHG measurements: The incident laser beam for the SHG measurements was generated by a Spectra Physics Maitai SP Ti:Sapphire oscillator whose central wavelength is 800 nm and repetition frequency is 82 MHz. The incident power was fixed at 50 mW and focused on the sample surface with a diameter of ~ 100 µm. The p-out and s-out configurations were adopted during measurement, which denote the arrangements where the analyzer polarization is parallel and vertical to the plane of incident light field, respectively. The polarization direction φ of the incident light field is adjusted by the rotation of the λ/2 waveplate driven by a rotating motor.

DFT calculations

To investigate the evolution of electronic and magnetic properties upon anion doping, we have performed spin-polarized density functional theory (DFT) calculations with the inclusion of spin-orbit coupling (SOC). The T’-BFO is simulated by using a 2×2×2 40-atom BiFeO₃ superlattice with monoclinic distortion. In addition, we used a 40-atom orthorhombic superlattice model with the virtual crystal approximation to approximate the O-BFOS. In these models, the lattice parameters are constrained onto the experimentally measured values.

Specifically, the spin-polarized density functional theory (DFT) calculations of BFO and S doped BFO are carried out using the Vienna Ab initio Simulation Package (VASP) ^{51, 52}. The exchange functional, Perdew, Burke, and Ernzerhof ⁵³ parameterized in the generalized gradient approximation was used with the energy cutoff of 520 eV for the plane-wave basis set. The ab initio calculation jobs were partially managed by the Quacc code ⁵⁴. It is important to include the Hubbard U correction for Fe-3d electrons. The former DFT studies ^{4, 55, 56} have shown that the Hubbard U of 6 eV is able to well reproduce the magnetic and electronic properties of T’-BFO or O-BFOS. Therefore, we have applied the effective U of 6 eV in all the calculations using the Dudarev’s method ⁵⁷. The spin-orbit coupling (SOC) is included in the DFT calculations to investigate the magnetic ground state. We use 40-atom BFO superlattices in the simulations, where the cell parameters were constrained to the experimental values and the internal coordinates were fully optimized to meet the energy criterion of 10^− 6 eV and the force criterion of 5×10^− 3 eV/Å. Because the magnetocrystalline anisotropy energy is a quite small quantity compared to system’s total energy, we have improved the energy accuracy to 10^− 7 eV when comparing the total energies between different magnetic structures. The k-mesh uses 4×4×3. We also tested with k-mesh of 6×6×6 and cutoff energy of 600 eV and found the magneto crystalline anisotropy energy is nearly not changed, indicating the calculations were well converged.

Data and materials availability

All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.

Conflict of interest statement

The authors declare no conflicts of interest

Acknowledgements

This work was supported by the National Natural Science Foundation of China (22371013, 52032005, 52372119), the National Key Research and Development Program of China (2018YFA0703700), the Fundamental Research Funds for the Central Universities (FRF-IDRY-19-007 and FRF-TP-19-055A2Z), the National Program for Support of Top-notch Young Professionals, and the Young Elite Scientists Sponsorship Program by CAST (2019-2021QNRC), the “Xiaomi Young Scholar” Funding Project. Use of the Beijing Synchrotron Radiation Facility (1W1A and 4B9B beamlines, China) of the Chinese Academy of Sciences is acknowledged. We thank the staff from BL07U and BL08U beamline of Shanghai Synchrotron Radiation Facility (SSRF) for assistance of XMCD data collection. Technical and human support provided by DIPC Supercomputing Center is gratefully acknowledged.

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Shear Strain Control of Multiferroic Magnetic Ordering for Giant Ferromagnetism

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