Strain gradient is a normal phenomenon around a heterostructural interface in ultrathin film, and it is important to determine its effect on magnetic interactions to understand interfacial coupling. In this work, ultrathin Pr0.67Sr0.33MnO3 (PSMO) films on different substrates are studied. For PSMO film under different in-plane strain conditions, the saturated magnetization and Curie temperature can be qualitatively explained by double-exchange interaction and the Jahn-Teller distortion. However, the difference in the saturated magnetization with zero field cooling and 5 T field cooling is proportional to the strain gradient. Strain-gradient-induced structural disorder is proposed to enhance phonon-electron antiferromagnetic interactions and the corresponding antiferromagnetic-to-ferromagnetic phase transition via a strong magnetic field during the field cooling process. A non-monotonous structural transition of the MnO6 octahedral rotation can enlarge the strain gradient in PSMO film on a SrTiO3 substrate. This work demonstrates the existence of the flexomagnetic effect in ultrathin manganite film, which should be applicable to other complex oxide systems.
Bangmin Zhang, Ping Yang, Jun Ding, Jingsheng Chen, Gan Moog Chow.
Magnetic Interactions with Strain Gradient in Ultrathin Pr0.67Sr0.33MnO3 Films.
Engineering, 2024, 40(9): 170-178 DOI:10.1016/j.eng.2024.04.014
With the development of techniques for the fabrication of high-quality films, low-dimensional materials have attracted a great deal of attention due to their fascinating properties and rich physics [1], [2], which include superconductivity in thin film [3], new phases induced around the interface [4], and enhanced magnetic properties [5]. Forms of interfacial coupling at the heterostructural interface include [6], [7] structural coupling, band bending, and charge transfer. Due to the small thickness of a thin film, which can be just a few nanometers, structural-coupling-induced gradual change in the lattice constant (i.e., strain gradient) around the heterostructural interface plays an important role in the properties of the material. This has been extensively exploited in ferroelectric materials [8] to obtain a large strain gradient, in what is termed flexoelectricity, for the design of nanoscale devices. However, the effect of strain gradient on magnetic materials (the flexomagnetism) is relatively rarely exploited [9], [10]. Experimental evidence of the flexomagnetic effect has been reported in BiFeO3 films [11], [12], suggesting that the magnetization is enhanced due to the flexomagnetic effect in the mixed-phase region of a BiFeO3 thin film with a large strain gradient. However, this field is still in an early stage, and both experimental exploration of the flexomagnetic effect in materials and investigation into its microscopic mechanism require further study.
Manganite with an ABO3 perovskite structure is a strongly correlated electron system with coupling between the crystal structure [13], [14], spin, charge, and orbital structure. To explain the rich physics of this system, it has been proposed that double-exchange interaction [15], electron-phonon coupling [16], [17], [18], and super-exchange interaction [19] are simultaneously present and compete with each other, establishing a delicate balance that determines the properties of the material. One feature of this type of material is the co-existence of ferromagnetic and antiferromagnetic phases in a single layer, which can be manipulated by external stimuli. For example, the magnetization may be different after field cooling (FC) versus zero field cooling (ZFC), which can be attributed to spin frustration/phase melting. Considering the sensitivity of manganite to its crystal structure, manganite film with different degrees of strain gradient is worth studying.
Perovskite manganite Pr0.67Sr0.33MnO3 (PSMO) is a strong correlated system with a high ferromagnetic transition temperature, and its crystal structure and magnetic properties can be changed by strain. The saturated magnetization and Curie temperature of PSMO films under different in-plane strain conditions can be qualitatively explained by double-exchange interaction and the Jahn-Teller distortion. However, the saturated magnetization of PSMO at low temperature after ZFC and 5 T magnetic field cooling (5T-FC) from room temperature is different and is proportional to the size of strain gradient. Combining further structural and magnetic characterization, it is proposed that the structural disorder from the strain gradient enhances the antiferromagnetic interactions and the corresponding antiferromagnetic phase, which changes into a ferromagnetic phase during the 5T-FC process. This detailed study suggests that a non-monotonous transition of the MnO6 octahedral rotation around the out-of-plane c axis in PSMO film on a SrTiO3 (STO) substrate contributes to forming the largest strain gradient with medium lattice-mismatch strain among the tested PSMO thin films on different substrates. This work demonstrates the existence of the flexomagnetic effect in ultrathin manganite film.
2. Experimental details
Ultrathin 8, 12, and 30 nm PSMO (bulk lattice constant a = 3.860 Å, 1 Å = 1 × 10−10 m) films were grown on (001) KaTiO3 (KTO; a = 3.989 Å), (001) STO (a = 3.905 Å), (001) (La,Sr)(Al,Ta)O3 (LSAT; a = 3.868 Å), (001) LaAlO3 (LAO; a = 3.790 Å), and (001) YAlO3 (YAO; a = 3.716 Å) substrates with different lattice constants by means of pulsed laser deposition (PLD; Neocera, USA), which can apply in-plane tensile/compressive strain to the respective PSMO films. During deposition, the substrate was maintained at 780 °C in a 200 mTorr (26.6 Pa) oxygen atmosphere. The energy density of the 248 nm KrF excimer laser beam used was 1.5 J∙cm−2, and the pulse frequency was 2 Hz. After deposition, the films were cooled to room temperature at 15 °C∙min−1. The crystallographic texture of the films was studied using a four-circle diffractometer at the Singapore Synchrotron Light Source (SSLS). The magnetic properties were measured using a superconducting quantum interference device (SQUID; MPMS®3, Quantum Design, USA), and the transport properties were measured using a physical property measurement system (PPMS; Quantum Design). For the ZFC (FC)-magnetic hysteresis (MH) loop, the film was cooled from room temperature to 10 K under a zero (5 T) magnetic field; then, the magnetic field was set to zero before the measurement. For the ZFC (FC)-magnetization-temperature (MT) curves, the film was cooled from room temperature to 10 K under a zero (100 Oe, 1 Oe = 79.57747 A∙m−1) magnetic field; then, the curve was measured at 100 Oe during the warming process. Scanning transmission electron microscopy/high-angle annular dark-field (STEM-HAADF) imaging was performed using a double aberration-corrected JEOL-ARM200CF microscope (JEOL, Japan).
3. Results and discussion
The crystal structures of the PSMO [20] films on different substrates were investigated using X-ray diffraction (XRD) (002) l scanning and (−103) reciprocal space mapping (RSM), as shown in Figs. 1(a)-(e). All films on KTO, STO, LSAT, and LAO exhibited a 00l orientation with good epitaxial growth, and no strain relaxation occurred. The PSMO (bulk lattice constant a = 3.860 Å) film on KTO (a = 3.989 Å) and STO (a = 3.905 Å) exhibited in-plane tensile strain with a shortened out-of-plane lattice constant; the film on LSAT (a = 3.868 Å) was nearly strain-free, and the film on the LAO (a = 3.790 Å) substrate exhibited in-plane compressive strain with an elongated out-of-plane lattice constant c. The measured lattice constants as a function of the lattice-mismatch strain are summarized in Fig. 1(f). Additional diffraction data is provided in Section S1 in the Appendix A.
Bulk PSMO is a ferromagnetic metal below its Curie temperature of approximately 280 K. For ultrathin film, the material’s properties may differ from those of the bulk material. The magnetic properties of the PMSO thin films, including the saturation magnetization and Curie temperature, were investigated by means of SQUID and are shown in Fig. 2. For all samples, the MH loops along the magnetic easy axis (out-of-plane for film on the LAO substrate and in-plane for the other samples) at 10 K were measured after ZFC and 5T-FC, respectively, with 5 T being strong enough to saturate the sample. As summarized in Fig. 1(f), although the saturation magnetization (MS) after both ZFC (MS,ZFC) and 5T-FC (MS,5T-FC) showed a similar trend, decreasing with an increase in the absolute value of the in-plane strain (either tensile or compressive strain), the difference, MDiff, between the MS,ZFC and MS,5T-FC exhibited different behavior: For the PSMO films on the LSAT and LAO substrates, the magnetization difference MDiff was almost zero. However, for the films on the KTO and STO substrates, the MS,5T-FC was obviously higher than the MS,ZFC, where MDiff was 38 emu∙cc−1 (1 emu∙cc−1 = 1000 A∙m−1) for the film on the STO substrate. Similar magnetization enhancement has been previously observed with a tunable exchange bias [21]. However, no obvious exchange bias was observed in the current work. The ratio ζ = (MS,5T-FC - MS,ZFC)/MS,5T-FC was used to characterize the magnetization difference, the mechanism of which is discussed below. The magnetization along the magnetic hard axis showed similar behavior.
Both the Curie temperature TC and the saturation magnetization MS reveal the intensity of the magnetic interactions [22]. The results regarding the trend in the TC with lattice-mismatch strain are shown in Figs. 3(a)-(d). The 100 Oe FC- and ZFC-MT curves were measured for all the films with a 100 Oe in-plane measurement field; the TC is summarized in the lower inset of Fig. 3(c). The TC of the PSMO film decreased with an increase in the absolute value of the in-plane strain, similar to the MS. According to a model considering double-exchange interaction and the Jahn-Teller distortion [23], the TC of PSMO bulk and thin film can be calculated using the measured crystal structure by means of Eq. (1):
where εB is the averaged bulk strain, εJT is the averaged Jahn-Teller distortion, α and Λ are fitting parameters that can be obtained from previous work [24], and T0 is the Curie temperature of the reference.
In the present case, the PSMO film on the LSAT substrate (which was almost strain-free) was taken as the reference. It was observed that, although the exact value of the calculated TC was different from the measured value, the calculated trend was the same as the measured trend (details are provided in Table S1 in Appendix A). This suggests that the intensity of the magnetic interactions in the PSMO film can be qualitatively described by the above model. It should be noted that the PSMO film on YAO was relaxed, and the magnetic properties were dominated by the relaxed part, as discussed below and shown in Fig. S2 in Appendix A. Considering the lattice constant of the relaxed part of the PSMO film, rather than the in-plane lattice constant of the YAO substrate, the Curie temperature of the relaxed PSMO film also fit the overall trend in relation to the averaged in-plane strain (not the lattice mismatch between bulk PSMO and YAO), as shown in Fig. S3 in Appendix A. The resistivity of these PSMO films showed the same trend as the TC: Films with a high TC had a low (high) resistivity (conductivity), as shown in Fig. S4 in Appendix A, indicating a strong correlation between the magnetism and transport properties. The insets of Figs. 3(a)-(d) show the temperature dependence of δ = (MFC - MZFC)/MFC from the FC- and ZFC-MT curves. For convenience of comparison, the dependence of δ on the lattice-mismatch strain at 10 K is summarized in the lower inset of Fig. 3(c), revealing the competition between the ferromagnetic and antiferromagnetic phases, as has been proposed for manganite [25]; and its trend is the opposite of that of TC.
Unlike the TC and MS, the ratio ζ does not have a simple relationship with the absolute value of the lattice-mismatch strain. One possible reason is that the magnetic field during the FC process aligns the ferromagnetic component, which cannot be reversed at low temperature after the ZFC process due to the large energy barrier with spin frustration. This scenario is similar to the appearance of a difference between the ZFC- and FC-MT curves. In order to clarify this situation, additional MH measurement was performed at 10 K after 1 T field cooling (1T-FC) for the PSMO film on the STO substrate. During the cooling process, a 1 T magnetic field was applied at 300 K in the film plane, far above the Curie temperature of these ultrathin PSMO films, which was strong enough to align the magnetic moment. However, the saturated magnetization after the ZFC (MS,ZFC) and 1T-FC (MS,1T-FC) loops was the same, which suggests that ζ is not due to the alignment of the ferromagnetic magnetic moment (i.e., spin frustration due to the competing antiferromagnetic and ferromagnetic interactions in the spin/cluster glass), and other factors must be considered. Since the magnetization reveals the intensity of the ferromagnetic interactions, the difference in the saturated magnetization after ZFC and 5T-FC suggested that an additional magnetic interaction was revealed by the 5T-FC process.
It is well known that the strain and octahedral rotation are essential parameters affecting the properties of manganite, which correlate to the material’s properties at the microscopic level [26], [27], [28], such as the bond angle, bond length, and electronic hopping amplitude among different manganese (Mn) sites. Previous experimental work [29] has shown that change in the strain and octahedral rotation can effectively modify the Curie temperature and saturated magnetization, as well as the existence of inhomogeneity in the octahedral rotation. If the averaged strain and averaged octahedral rotation were responsible for the observed difference in saturated magnetization, the ζ would show a similar trend as TC and MS, which differs from the experimental observation. Previous research has revealed that, around a heterostructural interface, interfacial coupling can induce a gradual change in the crystal structure [30], [31], resulting in properties that differ from those of both the parent components. This would be significant for ultrathin film. Inhomogeneity is a common phenomenon in real materials and has an important effect on the materials’ properties. Inhomogeneity was described by a macroscopic parameter in a previous theoretical study [32], rather than by the local strain and octahedral rotation, which effectively explained and predicted the related physical phenomena.
Next, the strain gradient [33] of the oxide film in a perovskite structure [34] was determined according to Williamson-Hall (W-H) plots. The W-H plots were obtained from the XRD θ-2θ peak widths (θ is the angle between the incident X-ray beam and the film plane). In Figs. 4(a)-(d), the peaks (001), (002), (003), and (004) from the θ-2θ scans are used to determine the inhomogeneous strain along the out-of-plane direction, which correlates to the strain gradient [35]. The inhomogeneous strain (εi) is defined as
where ε(z)is the strain profile, 〈ε〉 is the averaged strain of the whole film, t is the film thickness, and z is the coordinate along the out-of-plane direction. εi indicates the deviation of the crystal structure away from the averaged structure, which can be estimated from the slope of the fitted curve (the dashed line in Fig. 4(e)). In general, the larger the inhomogeneous strain, the larger the strain gradient. The current work refers to the strain gradient using the measured inhomogeneous strain [35], εi. It should be noted that, due to the closeness of the lattice constant between the PSMO and the LSAT substrate, the inhomogeneous strain could not be obtained from the above measurement and was estimated to be approximately 0. However, a larger lattice mismatch does not necessarily result in a larger strain gradient. The strain gradient from the W-H plot for the PSMO film on LAO was smaller than that of the PSMO film on the STO substrate, while the absolute value of the lattice mismatch was the opposite. In addition, Fig. S5 in Appendix A shows that the full widths at half maximum (ΔL) of the l scan around the (−103) peak are 0.052 and 0.055 for the films on the LAO and STO substrates, respectively, suggesting that the out-of-plane lattice constant c of the film on the LAO substrate was more uniform than that of the film on the STO substrate. The c might approach the averaged value quickly in a short distance along the thickness direction for the PSMO film on the LAO substrate, and then most of the film would have a uniform c, resulting in a decreased strain gradient in the whole film. Further discussion on the evolution of the strain gradient for PSMO on the STO substrate is provided below, in the discussion on octahedral rotation.
The measured εi is not proportional to the lattice-mismatch strain but has a close relationship with the ζ of the PSMO film on different substrates, as illustrated in Fig. 4(f). For the PSMO on STO, which has the largest strain gradient (εi = 0.11%), the ζ is the largest, at about 0.112 compared with those of the other films. Direct evidence of the strain gradient in a high-resolution scanning transmission electron microscopy (STEM) image is shown in Section S6 in Appendix A. The lattice constant of PSMO around the PSMO/substrate interface would be close to that of the substrate; it would then gradually evolve with an increase in the film thickness. During this process, the strain gradient develops. Based on the above analysis, the origin of the difference between the MS,ZFC and MS,5T-FC should be related to the strain gradient. It is notable that the ζ starts to increase after the inhomogeneous strain reaches a critical value of about 0.02%. The strain gradient is revealed as a non-uniform distribution of the atomic position, which can be changed by external stimuli in most materials. Hence, the method used in this work should be applicable to other systems.
Additional experiments with strain relaxation were done to verify the above argument. An 8 nm PSMO film was grown on a (001) YAO substrate with an in-plane lattice constant of a = 3.716 Å, and the XRD results showed that strain relaxation occurred with two components (the strained and relaxed regions) in the 00l scan, (002) RSM, and (−103) RSM, due to the large lattice mismatch. (A detailed data analysis is provided in Section S4 in Appendix A.) The averaged in-plane and out-of-plane lattice constants of the PSMO film were as = 3.716 Å and ar = 3.862 Å, and cs = 3.974 Å and cr = 3.824 Å, for the strained and relaxed regions, respectively. According to the (002) peak in Fig. 4(d), the peak intensity ratio of the relaxed PSMO (the larger θ, labeled as R) to the strained PSMO (the smaller θ, labeled as S) is 3:1, indicating that the main volume of the PSMO film is the relaxed part. According to Eq. (1) for the Curie temperature, the calculated Curie temperatures for the relaxed and strained PSMO are 242 and 162 K, respectively. The measured Curie temperature of the PSMO film on the YAO substrate is 246 K.
Based on the above discussion, we suggest that the magnetic properties of the PSMO film on YAO substrate are dominated by the strain-relaxed part of the thin film. For the relaxed part of the PSMO, although the in-plane a is quite close to the bulk value, the out-of-plane c is smaller than the bulk value. The reduced volume of the unit cell contributes to the relatively high Curie temperature [36]. For the strained part, the tetragonal ratio c/a is far from 1 with a strong Jahn-Teller distortion, which would decrease the TC according to Eq. (1). The corresponding strain gradient of the strain-relaxed region and the magnetic properties are summarized in Fig. 4(e). The ζ is 0.065 with an inhomogeneous strain of 0.06% in this sample, which is larger than those of the films on the LAO and LSAT substrates. The quite large difference in the out-of-plane lattice constant between the relaxed (cr = 3.824 Å) and strained (cs = 3.974 Å) regions may contribute to the relatively large strain gradient through interfacial coupling between these two regions, as has been proposed for a mixed PbO and PbTiO3 phase [37], indicating that strain relaxation could be used to induce a strain gradient in a nearly strain-free region. These results suggest that the strain gradient affects the magnetic interaction in both single-crystal and multi-crystal materials.
How does the strain gradient affect the magnetic interactions and corresponding magnetic properties in manganite film? The strain gradient breaks the spatial inversion symmetry of the crystal structure, causing electric polarization [8], [38] (the flexoelectric effect). However, magnetism comes from the breaking of the time-inversion symmetry, and the strain gradient cannot induce the flexomagnetic effect [39] directly. In manganite, different contributions—such as double-exchange interaction, phonon-electron interaction, and super-exchange interaction—work together to determine the material’s properties. Previous theoretical work has shown that quenched disorder (Δ) [4], [32] in the interaction’s intensity has a similar effect as enhancing the phonon-electron interaction, which tends to decrease the electronic hopping probability, inducing a metal-to-insulator phase transition even with the existence of only ferromagnetic interactions. The quenched disorder also has a similar effect as enhancing the antiferromagnetic interaction [40] to induce a phase transition. In addition, the effect of disorder on the material’s properties can be suppressed by a strong magnetic field. With the strong correlation between the magnetic and transport properties in manganite, an increase in resistivity coincides with a decrease in the hopping probability of electrons, which weakens the ferromagnetic interactions. According to the definition of inhomogeneous strain, the strain gradient in PSMO film can be viewed as a deviation (structural disorder Δ) from the averaged structure (lattice constant, octahedral rotation, etc.), as illustrated in the inset of Fig. 4(f), which has the effect of enhancing the phonon-electron interaction and antiferromagnetic interaction.
During the ZFC process, the magnetic moment tends to be randomly orientated from room temperature to 10 K. Under 5T-FC from room temperature to 10 K, the magnetic field aligns the magnetic moment for both the ferromagnetic and antiferromagnetic phases above the magnetic ordering temperature, which can be restricted to 10 K. The aligned moment by the strong 5 T field during the cooling process facilitates electronic hopping among the cations and ferromagnetic interactions, and induces an increased net magnetization, compared with that under ZFC. For the PSMO film on the STO substrate, which has a large strain gradient and enhanced antiferromagnetic interactions, the suppression of ferromagnetic interactions by the strain gradient is large. The strong 5 T magnetic field during the cooling process aligns the magnetic moment toward the direction of the magnetic field, facilitating electronic hopping among the cations and increasing the net magnetization. In contrast, for PSMO with a low strain gradient, the effect of the cooling field decays. It should be noted that the magnetic field required to suppress this effect is approximately on the Tesla scale, according to a comparison of the MS,ZFC ≈ MS,1T-FC < MS,5T-FC. For other films with a decreasing strain gradient, the ζ decreases as the effect of disorder on the magnetic properties decreases. It should be noted that enhancement of the MS can occur in both metallic (i.e., YAO sample) and insulator (i.e., STO and KTO samples) film.
Another question is how the strain gradient develops in film. From the above results, the lattice mismatch between PSMO and LAO is larger than that between PSMO and STO, but the strain gradient for the PSMO film on STO is higher. Hence, the contribution to the strain gradient is not determined only by the lattice mismatch, and additional factors should be considered. It has been reported that both the lattice constant and the octahedral rotation [41] can work together to modulate the lattice-mismatch strain. Additional work was therefore performed on PSMO film with different thicknesses (12 and 30 nm) on LAO and STO substrates, respectively. For the YAO and KTO substrates, strain relaxation occurs in thick PSMO film due to the large lattice mismatch, which would complicate the development process of a strain gradient. For the LSAT substrate, the octahedral rotation pattern of the PSMO film cannot be measured via half-integer diffraction, due to the overlapping signal from the substrate. With an increase in the film thickness on the STO substrate, the measured inhomogeneous strain εi and the ζ decrease, as shown in Fig. 5, suggesting that the effect of the strain gradient decays with increasing film thickness.
The MnO6 octahedral rotation of the 8 nm PSMO film on an STO substrate was measured via half-integer diffraction and was found to be a-a-c+ according to Glazer’s notation [42], as shown in Fig. 5(c). The rotation pattern was a-a-c- for the 12 and 30 nm films [4], [42]. Around the STO/PSMO interface, without the octahedral rotation of TiO6 (a0a0a0) in the substrate, the MnO6 rotation was suppressed, due to the connectivity of the octahedra, which results in a large Mn-O bond angle with an enlarged lattice constant around the interface, as has been shown via STEM [4] in previous work. With an increase in the film thickness, the MnO6 rotation evolved from a0a0a0 (around the PSMO/STO interface) to a-a-c+ (8 nm film), and then to a-a-c- for the 12 and 30 nm films, as illustrated in Fig. 5(e). In all thicknesses, the in-plane lattice constant was fully strained by the substrate. Based on the half-integer diffraction results, the octahedral rotation does not translate directly from a0a0a0to a-a-c- with an increase in the film thickness; there is an intermediate MnO6 rotation pattern, a-a-c+, in the 8 nm PSMO film. In order to maintain the octahedral connectivity, the MnO6 rotation around the out-of-plane c axis may evolve from c0 to c+ first; then, the in-phase c+ rotation should decrease to zero (c0) before the transition to the out-of-phase c- with an increase in the film thickness. Due to mutual accommodation between the lattice constant and the octahedral rotation, the non-monotonous transition process around the out-of-plane c axis (as illustrated in Fig. 5(c)) can only modify the out-of-plane lattice constant, which might introduce an additional contribution to the out-of-plane inhomogeneous strain (i.e., strain gradient), and then increase the strain gradient, compared with the situation of a monotonous change in the octahedral rotation. Such an enhancement in the strain gradient by an elastic wave has been investigated in a flexoelectric system [43], [44]. The strain gradient is a macroscopic parameter that describes the changes in the strain and in the oxygen octahedral rotation (a local microscopic parameter) in thin film, which are intrinsically coupled. However, a discussion on the effect of the local strain and local octahedral rotation through the whole film at the atomic level requires further study.
Similar measurements were done for PSMO film on an LAO substrate. For each of the 8, 12, and 30 nm films [45], the rotation pattern was a0a0c-. The absence of rotation around two in-plane axes made the out-of-plane Mn-O bond angle 180°, which modulated the enhanced out-of-plane lattice constant compared with that of the bulk materials. The AlO6 in LAO had an a-a-a- rotation, so the MnO6 rotation at the LAO/PSMO interface was affected by the AlO6 rotation due to the octahedral connectivity. The unchanged rotation pattern in all the thicknesses suggests that the film may approach a stable structure (a0a0c-) in a short thickness range, and the transition of the octahedral rotation is monotonous from a-a-a- to a0a0c-, which might cause a relatively small strain gradient in the PSMO film compared with that on an STO substrate, although it has a higher lattice mismatch. The different behavior of the strain gradient of PSMO on LAO versus STO is likely to stem from the difference in the lattice-mismatch strain and the octahedral rotation inside the substrate, which affect both the lattice constant and the octahedral rotation of the thin film.
While this “camouflaged” effect of the strain gradient on the magnetic interactions is not displayed explicitly, it is revealed by a strong magnetic field. This elastic-magnetic coupling in functional materials is an example of the flexomagnetic effect, whose microscopic mechanism is the disorder-induced suppression of ferromagnetic interactions. Similar to magnetostriction and stress-induced magnetism, this elastic-magnetic coupling is likely to be related to the spin-orbital interactions in the materials. Hence, in order to obtain a large flexomagnetic effect in functional materials, future work focusing on systems with large spin-orbital interactions and a non-monotonous transition in the structure would be useful. In addition, with the increasing importance of heterostructural interfaces in device fabrication, this work provides another contribution to the experimental control of magnetic properties, which can be applicable to other systems with both metallic and insulating materials.
4. Conclusions
In this work, the properties of PSMO film on different substrates were systematically studied. The saturated magnetization and Curie temperature of PSMO film under different degrees of strain were qualitatively explained based on double-exchange interaction and the Jahn-Teller distortion. However, the difference between the saturated magnetization under ZFC and that under 5T-FC is proportional to the strain gradient, which affects the saturated magnetization via disorder-related magnetic interactions. The non-monotonous structural transition contributes to the large strain gradient of PSMO film on an STO substrate. This work demonstrates the existence of a flexomagnetic effect in ultrathin manganite film.
Acknowledgments
The research was supported by the Natural Science Foundation of Guangdong Province of China (2023A1515010882) and the Large Scientific Facility Open Subject of Songshan Lake, Dongguan, Guangdong Province of China (KFKT2022B06); the Singapore Ministry of Education Academic Research Fund Tier 2 (MOE2015-T2-1-016, MOE2018-T2-1-019, and MoE T1 R-284-000-196-114), and the Singapore National Research Foundation (NRF-CRP10-2012-02). Ping Yang is supported from SSLS via National University of Singapore Core Support (C-380-003-003-001).
Compliance with ethics guidelines
Bangmin Zhang, Ping Yang, Jun Ding, Jingsheng Chen, and Gan Moog Chow declare that they have no conflict of interest or financial conflicts to disclose.
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